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Champion Graveyard Sound

Macro photography and fractals have a lot in common.  I don’t know what that is, but I just sense that they have a “family resemblance”.  Imagine you’re trying to put together a jig-saw puzzle but someone has accidentally thrown in another puzzle with it.  While looking for the pieces that match up with the ones you’ve already put together you’re also picking out the ones that belong to that other puzzle that don’t belong in the same box.  But you also keep coming across pieces that, while they don’t fit in immediately with the small part you’re already assembled, you sense they’re part of the larger complete picture and you want to hold on to them and not put them aside with the pieces of the other puzzle because they look, in some vague and hard to describe way, similar.

Haven’t we all zoomed into something like this in a fractal program?  This fly’s head reminds me of many of the formulas in Sterlingware.  Flies are purely a nuisance when seen at a regular scale but they are both magnificent and terrifying when seen up close.

I got these two fly photos off the Wikipedia.  This second one here is really a work of art.  I like color and I think color almost has a subliminal thought-inducing language and quality all its own.  What an incredible machine the common housefly is; no spaceship or aircraft a human could design will ever look as superb as this housefly.

10 Million Year-Old Fractal Found in Antarctic Ice! According to a recent article in the Scientific American, some ancient species of molds when allowed to grow slowly and undisturbed for millions of years, grow and develop in patterns that are identical to those formed by iterating fractal formulas with a computer.

I just made that up, but that’s what I thought when I saw this image by Jesse in the Fractalforums.com gallery.  Great images just make me want to say great things.  The facts come later.

The mandelbrot inside the mandelbox!  But it seems only natural to find a mandelbrot man inside a mandelbox 3D fractal formula.  He lives there.  Just like a pearl inside an oyster and it’s shell.

I’ve looked at this image quite a bit and I can’t decide if it looks more like the mandelbrot is being absorbed by the mandelbox, as I think the title by lenord is suggesting, or if the mandelbox is actually growing out from –and growing off of–  the mandelbrot just like a plant grows out of a seed.  Lenord’s got some other ones like this and they have the same interesting combination of old and new fractal designs.  Apparently it’s all from the same formula and not from layering or some sly photoshop trick.

New people are always popping up over at Fractalforums.  Fractalforums seems to be where all the action is lately.  I don’t know who any of these people are (and they don’t know me) but I don’t really need to know them when I can just look at their work and judge it for itself.  Tatty has really come up with something new here.  So much detail and such variety of it.  But it doesn’t look like a mandelbox or mandelbulb to me and yet it has that 3D look to it.  Could there really be some new thing called a “Kractal”?

Another by Tatty.  Already she’s developing some noticeable style just in these two images.  There’s a wide variety of shapes and yet they complement each other instead of clashing or looking pushed together.  Subtle and with good coloring too.

Box 1? If this is just the first she’s off to a great start.  Tatty has a good eye for the sort of pleasing organic shapes that fractals excel at.

I followed a link from Mandelwerk’s Deviant Art page to these incredible mandelbox images by Janetino.  Janetino has such unique color palettes.  I’ve never seen any mandelbox images with this sort of coloring that looked so good.  Nice use of the foggy perspective effect here too.

This one is really something.  So ornate and such unique color.  The blue haze suggests sky and sunlight streaming into this ornate temple or ritzy spaceship.  I’ve got to look around Deviant Art more.  It’ll be worth it if I find another artist with such unique and well done work as Janetino.  She’s up there with the other top “Mandelboxers” in my opinion.

Here’s an interesting photo for two reasons:  First, because it has such a dreamy, visionary, summer night, sky full of imagination and wonder look to it.  Second because it’s actually a photograph of the Hiroshima atomic bomb explosion taken, not from the air, but from the ground several miles away by a civilian who just happened to be in the right place at the right time.  It dulls the golden glow of the photo’s dreaminess to know we’re also observing an event that killed over 100,000 people in less time than it takes to answer a ringing telephone.  I wonder how many other attractive things in our world would look less appealing if we knew what we were really looking at?

Texture was found on the Fractalforums.com gallery like many of the images here.  The gallery contains (I believe) any images uploaded to the forum for any purpose, either artistic or as examples and illustrations in technical discussions.  I can’t always tell what context the image appears in with respect to the forum postings, I just browse the image gallery in behind the scenes mode and comment on whatever catches my eye.  I like this one for it’s simple, classical fractal style.  Sometimes less is more and this is a good example.  This image has a real sense of style and stands out because of it.

Just like Texture this image features imagery that isn’t new and cutting-edge like the mandelbox or mandelbulb and yet has real style and focuses on the more classical fractal type of imagery.  I think this has an extra layer, a grid pattern over it and although that might seem rather simple the effect it has on the image is strong.  It looks like it could have been taken off a vintage pulp sci-fi cover and maybe the author thought the same thing when he named it.

This image really has to be seen in full-size which you can do by clicking on it.  The mandelbox, like most fractals, is capable of producing a lot of imagery but it takes a good eye and some careful experimentation to produce something of interest amidst the deluge of images that pour out of the formula  This one has a surreal look to it.  Maybe it’s the ornate architectural appearance that makes the square “front desk” of the mandelbox lobby look real and therefore strangely out of place.  The fact that it’s sunk below the horizon and hidden from sight enhances the eerie feel.

I hear this Borg thing mentioned here and there but I don’t know what it’s about or what it’s from.  I find it odd that a Cyclops would be making 3D art, but maybe that’s just a screen name for L. Shone?  There’s an MC Escher look to this and I like the careful, repetitive metallic detail in it.  The hole in the center is a nice touch and shows us that the inside is remarkably no different than the outside.  It’s got an old, engraved illustration appearance that I like.

Another one that I’d call “classical”.  I guess I’m referring to fractal imagery that is single layer and was much more common back before multi-layered programs like Ultra Fractal came out.  But… this one was apparently made with UF!  I’ve always liked the shiny tubes and other orbit trap kinds of imagery that have an almost collage look to them.   The abrupt transitions resemble cut paper but sometimes the tube forests stretch all the way to the horizon although they do look like the scissors lopped off their upper branches, swift and invisible.  There can be a lot to see in these apparently simple images.  Good art is like that.

I check in on the Fractalforum.com gallery everyday.  When I saw the first of these Orion images I frowned a little because it reminded me of when I first started out making fractal images in Sterlingware almost a decade ago.  Later on, after seeing this one and especially the jagged, machine made elements surrounding it, I began to see the subtle but attractive style that these Orion images have.  This is pure digital vision; it’s all machine made and it shines with a technological glow like only some bold new discovery in a laboratory can.  The machine drew this and no human hand can imitate that cold, fractonic style.

One last one.  This is a real photograph of Titan, the largest of Saturn’s moons.  I think it’s made up of several shots taken by more than one pass of the space probe although it lacks the jumbled, collage look of a composite photo.  I’ve been using this image as my desktop wallpaper for almost a week, centered with a black background.  I keep thinking it’s the opening shot from some vintage, 1950s sci-fi film that’s about to begin:  Sinister Planet.

Anyhow, those are the pieces of the puzzle.  Maybe some of them don’t belong to the same big picture.  Or maybe this puzzle is a lot bigger than the 10,000 piece label on the box says.  We should have started building this on the floor instead of the table.

Frames, drains and hurricanes

Many people have a favorite sport.  Some follow soccer, others american football or hockey, basketball, baseball, cricket…  I follow hurricanes, the tropical storms or cyclones that form in the Carribean during summer and fall of every year.  There’s never a players strike and you can follow all the action over the internet.  In fact, you really don’t want to buy tickets to see any of these “games” live.  The American National Hurricane Center gives you the best seat in town, or out of town, rather.  There’s only one team but everybody loses.  And it’s impossible to cheat.  It’s a funny sport.

This year was supposed to be much more energetic, which was a great relief after the incredibly disappointing 2009 season.  I’m still waiting for a really big, Category 4 or 5, game this year.  Bonnie was so pathetic the NHC stopped talking about her before she even made landfall which, in this game, is ordinarily the main event.  She just went back to being a depression –tropical depression.

They don’t name them only after women anymore, they’ll use any name.  They ought to let the folks living in the path of the hurricane suggest the names.  But they’ve got more important things on their minds –hiding, dodging, staying alive.

Life is the sport of sports and art is its World Cup.  But that’s coming from a guy who thinks hurricane season is more fun to watch than the SuperBowl.

Back to fractal art:  here’s a piece of fractal artwork by Deviant Art member Sophiiiii that caught my eye just this week and also strongly suggested –hurricane– to me.  (That’s Sophi with five “eyes”.)

- Click on any of the images below to view them full size and on their original site -

This image (by “Five-Eyed Sophi”) has a number of interesting aspects.  Although, from the title, she probably didn’t intend it to have a marine theme much less that of a hurricane, it fits well into this and I think she saw a similar terrifying weather theme from her choice of the word, frost.  But maybe the spider web is the terrifying theme here?

I guess that’s the thing with “imaginary” art: the image is open to a number of interpretations, each one arising from the personal context the image unavoidably becomes mixed up in when it engages the viewer’s mind.

It was made in Incendia and I suspect has a few other layers incorporated into it, such as the spider web and the cloudy, watery background.

As I was saying about hurricanes, they are “wrathful” creatures that arise almost out of nothing and quickly grow (within days sometimes) into massively destructive beasts.  They are also composed, not of a neat circulation pattern which we see in the simplified diagrams used to explain them, but of broken and winding bands of thunderstorms and sometimes tornadoes spawned by those thunderstorms.  Sophiiiii’s image here, although completely artificial, is an excellent example of such an “extreme weather phenomenon”.

And it looks good too.  Incendia seems to have this nice ability to make grainy images that are more characteristic of real world imagery than the slick smooth world of computers, but I think Sophiiiii has added a lot of her own artistic talent to make this one looks a well as it does.

Sure.  This one’s not a fractal.  But when you’re floating in the ocean off the coast of Quintana Roo where Mexico meets Belize and the rest of Central America, such things are incidental.  There is the hint of shore in the dark bottom we see through the water, but where is it?  This is the morning after the hurricane.  It’s beautiful.  Out there somewhere is your house, but take heart, there’s plenty of building materials all around you.  One of them must have hit you and knocked you out.

I read an anectdote about hurricane Hattie that erased Belize City back in the 60s.  The author, a young boy at the time, told about how his family had completely lost their house (built on the beach, incidentally) but then a week later his father and uncle were out fishing and found a better one that the storm had dropped off from somewhere else.  I’ll bet there’s a lot of that shuffling of property going on in the wake of hurricanes every year.

Obviously this isn’t a fractal either, but Peter Alexander has made palm trees into such a separate and well developed genre much like the fractal spiral is in fractal art that they deserve a mention.  Click on the image to see the whole collection.  Very colorful.  I had a hard time picking the best one because they’re all very interesting.  Monoprints are prints that are made with unique characteristics and thus not reproducible merely by making another impression with the plate.  (I’ll bet they sell for more too.)  I think the coloring here is very sophisticated and carefully done.  I don’t like a lot of contemporary art (of the paintbrush sort) but these palm trees are something completely different.  Better than Warhol?

This one is just fantastic.  Color, shadows, lighting, contrast; it’s like a carefully painted old master’s work, laboriously rendered and painstakingly perfected.  That’s what Incendia can do when the right person is clicking it’s buttons.  I guess it’s a bit like paintbrushes: what comes from them depends on who’s holding them.  This is sort of weird, but I think the real beauty of this work is in what the image is reflecting.  It’s the light source that we don’t see.  There’s something golden, shining and radiant in this image –off screen– and it’s all suggested by what we see in the image.  The question is not, “What is this?” but rather, “Where are we?”  This is a great place.

To me this image is sea shells and other sea debris caught in a tangle of branches on the shore after that world cup of storms –a hurricane.  Neatly collected, I see.  Apparently the best time to collect sea shells is right after a storm (the key word is “after”).  That might also be the best time to check and see if your neighbors are still alive, so you’ll have to chose between the two.  Of course if your neighbors are down on the beach… with the seashells…

Sophiiiii added a link on her Deviant Art page to the image she used as the background for this image.  It’s worth looking at too.

I find it interesting how the background complements the incendia image.  It may seem trivial, but the background layer, even just a colored texture like this, just like the frame on a painting, is part of the artwork and contributes to the viewer’s general impression in ways which I suspect can be quite strong even if they may appear subtle at first glance.  Speaking of frames…

What came first?  The Picture or the Frame?

Flickr’s thesmartestfish (Sophia Brueckner) said “experimenting with some vintage round picture frames I bought on etsy. I was thinking it would be interesting to have a series of paintings in round frames. not sure if I want to keep going in this direction though.”

(Etsy.com apparently is a website that describes itself as “Your place to buy and sell all things handmade, vintage, and supplies.”)

Thesmartestfish really is pretty bright.  Not only is she a Master of Fine Arts student, she also works with javascript to create generative imagery using the Processing platform; a nice combination of skills we could all use.  From this I suspect she either printed and embellished by paintbrush the images in her round collection (similar to monoprinting) or just painted them freehand using their simple but characteristic, generative look as a guide.  Either way she’s produced something quite appealing.

Here they are; nicely photographed, too.

The round paintings look hand-painted but the bottom image the author describes as “shapes generated by javascript + photoshop with a scanned watercolor background.”

It’s a strange dynamic between frame and picture but there’s more dynamism going on.   Consider the interplay between the digital imagery of the javascript-photoshop process and thesmartestfish’s own hand painting skills.  Thesmartestfish created the javascript which in turn produced the snakey tendril imagery.  But that computer generated imagery in turn went on to inspire the hand made images in the round picture frames.  From such well defined and synergistic rotation often comes a powerful hurricane.  But it has to stay well out at sea, away from land, and feed on  warm waters and also avoid the vertical shearing forces of interfering ridges and troughs which dissipate the force of that rising energy coming off the sea.  Hey, some people like to talk in football or baseball analogies.  I prefer hurricanes.

Finally, everything flows back to where it came.  Solomon remarked on this very thing almost three thousand years ago: “All streams flow into the sea, yet the sea is never full.  To the place the streams come from, there they return again.  All things are wearisome, more than one can say.”

Ouch.  Here’s a fine illustration of that somewhat depressing/encouraging quotation.  It’s in the form of a video screen capture of a highly talented java applet rendering Fractal Drainage Patterns.  This is extremely fractal.  But I doubt it would have cheered up Solomon: everything is just sinking into the earth and if you watch the applet long enough at the original site, everything eventually fades into nothing.

I think they’re cool.  They’ve got a weird, sci-fi, Andromeda Strain replicating space-virus look to them.  I suppose epidemics and even wars have similarities to sports, just like hurricanes season does.  But hurricane season has a much more regular, reliable schedule than those other disasters even if all the hurricane game dates are impossible to predict ahead of time except by more than just a few days.  I should go check right now.  There’s a new update at the NHC about every four hours.  The next big one could be boiling away as we speak.

Surf’s up

I’ve been surfing.  From the noisey beaches of Deviant Art to the silent shores of guano islands.  Every one here’s a gem to me.  Each one gleamed in its own way when I saw it.

Remember this:  There are things that can be bought for a few glass beads in the South Seas that can be sold for a king’s ransom back in Amsterdam.  But remember this also:  there are things that can be bought for a king’s ransom in Amsterdam that are worth nothing more than a few glass beads in the South Seas.

Click on any of the images to see them full-size and on their original website where you can browse more works by the artists.

Dave seems to make a very wide variety of fractal imagery and works almost entirely, I believe, in Ultra Fractal.  I’ve never seen anything quite like this.  A city of dreidels?  The surface texture suggest some old kind of nylon material.  There’s a strange vintage radio tube feeling to it.  Nice, subtle coloring that reinforces the 20s or 30s Art Deco style (before the time of brightly colored plastics).  A rather unique image with a similarly unique style.

Strange electronic vibes and I like strange electronic vibes.  Perhaps an unusual image to draw attention to, but who cares about the usual images?  I suspect this one was uploaded as part of a Fractalforums.com discussion, but that just adds to it’s exotic allure.  Maybe Bent-Winged Angel wasn’t trying to make a piece of art with this one, but she did.  It splashes like water but turns into grains of sand around the edges.  Far out.

Talfrac adds that the image was made with Fractal Imaginator.  This is a program by Terry Gintz that I’ve never tried.  I like the clean, solid, silkscreen rendering style that the image has.  Sharp, crisp colors.  Anyone familiar with fractals will recognize the common organic structure to the image despite it’s very untraditional –vector-like– blocky rendering style.  This looks more “art gallery” like than most of the smooth, millions of colors fractal images normally seen.

Full color or black and white, a good image is simply a good image.  Art’s funny that way.  Working with the most advanced and feature rich formats doesn’t guarantee anything.  Of course there’s nothing simple or retro about this image here by Samuel Monnier.  It’s another example of his sophisticated pattern piling technique that he’s been polishing over the years and developing with Ultra Fractal.  Click on the image to go to the original site where you can explore the vast algorithmic world which we are only seeing as a mere thumbnail here.  There’s  so many interesting things to see in this one.  It’s like a table of contents for a large anthology.

This is a mandelbox, I’m guessing.  Not your average type of mandelbox and not the usual style.  Strong design is what makes this one special.  Everything lined up and arranged in a careful display of shape, form and symmetry –but with the usual mandelbox variations and complexity to it.  Look closely, is it really symmetrical?  anywhere?  All an artist really does is help us to see the great scenes going on around us that us common folks don’t seem to notice.  I think that’s what Lenord’s done with this one: he’s helped us to see the simple shapes and the sophisticated patterns made in the mandelbox by cutting out all the usual distractions of surface texture and wild, vast perspective.  Yes, art is complex, but only when you analyze it.  Out in the wild it’s natural and instinctive.  But that’s why it sneaks past us so easily.

What are those men doing in a fractal?  Believe it or not, this is actually a photograph of a very elaborately designed pipe organ somewhere in Spain.  Or maybe it really is a fractal and the author cleverly edited the image?  Never let your right eye know what your left eye is looking at.

I often feel that fractal art is not really about fractals but is instead about “imaginary” imagery.  In that sense, there are many “pre-columbian” fractals out there; meaning they are graphically similar although completely unrelated in terms of the way they were made.  Fractals just make it easier to create imaginary imagery.  I guess it depends on how you chose to define the art form.  The lack of a fractal formula naturally makes it hard to call  “fractal”.  Well, in the old days fractal artists worked hard.  Try doing something like this.

This one’s for real.  I stumbled on Kaeltyk’s Deviant Art gallery somehow.  I forget how.  Maybe from a link in someone else’s favorites?  Incendia does some nice things, but I’ve never seen such a good combination of 3D and 2D elements like there is in this one by Kaeltyk.  And it’s black and white, too.  Black and white is a whole new kind of color.  The uber-color.  It’s often thought of as being being feature-poor as opposed to feature-rich.  But all the colors in the world can’t do what black and white does.  More strangeness.

This one by Kaeltyk was done in Ultra Fractal.  I just like these peaceful drifting snowflakes and the different landscapes they seem to be falling and dissolving into.  It’s hard to crop out just the right piece from among such a huge mass of repeating imagery like this, but Kaeltyk did a good job here.  Very professional looking.  It deserves a classy title and black frame.

I would have guessed Incendia for this one, but Kaeltyk’s notes for this one indicate it was made with Xenodream.  I know these sorts of spirally seashell/horns are common and perhaps even cliche now, but Kaeltyk has managed to create something interesting and appealing even in such a heavily picked over genre.  In Kaeltyk’s own words, “I like how it’s clean and almost carved.”  That’s why I like it too.  The coloring and surface texture adds a lot as well.

According to notes for this image it was made by “two pictures of the sky that I merged together and then reversed”.  I guess the inverting created the yell0w-orange coloring from the natural blue sky tones in the original.  I include this because it’s another “mind-bender” that show that when we look at graphical imagery and ignore how it was made, we find “fractals” in places we wouldn’t have expected.  Although the shapes and structure of clouds really are a natural form of fractal rendering.  I guess that just reinforces my point.

“FMF + POV-Ray”  POV-Ray is a ray-tracing (ultra realistic) program, but I’m not sure what FMF stands for.  I like planetoids and this one’s got some cool coloring and texture.  Looks like ice cream that’s just about to start dripping.  Incidently this was chosen for a Fractal Window Weekly on Renderosity a year and a half ago.  I visited cgpad.com, the so-called Chinese Fractal Art Society and I think maybe Ferry Man Fractal is the mysterious “FMF”.  I’ve never heard of the program, so maybe spanzhang made it himself?

By spanzhang again.  He’s got a gallery at span.cgpad.com.  This one’s made with Apophysis.  Nice design with repeating circular elements and good colors.

Yes, people used to dream of such imaginary, fractal-like imagery way back in the 70s.  But it’s not merely once in a lifetime today; it’s everyday and all the time.  Music’s gotten a lot cheaper now too.  Hasn’t it?  And who needs to pay to get great artwork for their album covers nowadays with all this computer made stuff around?  “And you may ask yourself…” how come nobody sings about having mental breakdowns and emotional decay anymore?

Check out the nice set of instructions Shala has made to go with this example of Fractal Earrings.  “Fractals are geometric patterns that show self-similarity, they can be very complex and really beautiful.”  Doesn’t that statement by Shala answer the proverbial, “What are fractals?” question quite nicely?

You can also bead fractals. This is a pair of earrings that uses a very simple fractal pattern to create a delicate fringe or tassel that resembles some of the fractals you can see in nature like trees or the veins in your body.
The shape I used was 3 lines. Each time you add another set of 3 lines to the ends of the lines, that’s called an iteration.

For folks like myself such descriptions are more enlightening than those of the more technical type.  You’d think by now I’d know what a fractal is.  But I keep finding fractals that don’t fit the formulas.  Never let your left brain know what you’re right brain is thinking.

You’ll only end up slapping yourself in the face.

Art imitates Nintendo

I don’t play video games much; just an hour every day of Star Wars Battlefront (original one).  I have friends in Mos Eisley and although they always lose –horribly– they’re always asking me to come out and “play”.

My nephew loaned us his old GameCube and while I’ve never used it because all we have for it are Super Mario games, it’s been there on the floor in front of the TV for almost a year now.   I glance at it occasionally in between ferociously savage bouts of Battlefront ( Dark Trooper… Rhen Var Citadel…shotgun in the sky).

Since the discovery of the Mandelbox by Tom Lowe (Tglad) early in this year with it’s general cube formation and multiple grid and curved structures in it, I’ve looked at the Nintendo Gamecube differently.  They seem to be derived from the same formula.  Could it be true?

Exploring the graphical output of fractal algorithms should give you a floating feeling from time to time as you experience that “I don’t think we’re in Kansas anymore” feeling that Dorothy did when she found herself in Oz.  The world of video games is not so different either;  they’re as real as any movie you can see on your TV screen.  What we find in fractal graphics today would have passed for pure science fiction in the past.  What else?  3D fractals are the best game in town.

Anyhow, I just keep looking at that GameCube and can’t help but notice the resemblance to the Mandelbox.

Weird Scenes Inside the Goldmine

There’s actually a lot of goldmines out there in the outer reaches of our computer system.  None of us have been to all of them, but we’ve all been to some of them.  I don’t know where exactly this one is, but you can find all the scenes from it here.

This is what’s written at the entrance to the mine:

A gallery of large graphs

graph drawing of matrices in the University of Florida Collection

Graph visualization is a way to discover and visualize structures in complex relations. What sort of structures are people who do large scale computation studying? We can get a glimpse by visualizing the thousands of sparse matrices submitted to the University of Florida Sparse Matrix collection using sfdp algorithm . The resulting gallery contains the drawing of graphs as represented by 2328 sparse matrices in this collection. Each of these sparse matrices (a rectangular matrix is treated as a bipartite graph) is viewed as the adjacency matrix of an undirected graph, and is laid out by a multilevel graph drawing algorithm. If the graph is disconnected, then the largest connected component is drawn. The largest graph (Schenk@nlpkkt240) has 27,993,600 vertices and 366,327,376 edges. A simple coloring scheme is used: longer edges are colored with colder colors, and short ones warmer. The graphs are in alphabetical order. Use the “Search” link to find graphs of specific characters.

from: http://www2.research.att.com/~yifanhu/GALLERY/GRAPHS/index1.html

Thanks to but does it float for helping me find the Goldmine.

Bow the Knee to Blob!

Such simple rendering and yet, such powerful rendering.  Remember, most of MC Escher’s great drawings were done in pencil, so there’s no reason why a grayscale or monotone image has to be dull.  Just look at the detail in blob’s image, how it’s all over the place in every nook and cranny and has such creative diversity.  This is the magic of great software and those who know how to get the most out of it.

It’s made in Jesse’s Dierks’ free program, Mandelbulb 3D 1.53.  The expression, “the proof of the pudding is in the eating” really applies to fractal programs: you can judge them by what users are able to make with them.  As you can see here, Jesse’s program is clearly top notch.  I’m really surprised that such high quality software continues to be made in the fractal world.  I guess the new 3D formulas have inspired programmers like Jesse to create these new things.

Here’s another in the same palette but with more of a carved ivory look to it:

Again, subtle rendering that magnifies the beautiful designs of the hybrid mandelbox/sierpinski formula.  The top left corner I find to be the most interesting, next to the large round cavity in the center.  Everywhere you look there seems to be something a little different.  I’ll bet one could get completely lost exploring this object and forget all about taking snapshots.  Makes the Grand Canyon look like a ditch.

Just to show some contrast in rendering styles, take a look at these two by Kraftwerk:

This is no pencil drawing, but the lavish gold and metallic emerald surfaces look good in this mandelbox.

In his own words:

This is just too much for me, found this yesterday evening, sitting in the garden sun, two different worlds…

These formulas really makes you feel that they are designs from another world… first time I feel that mathematics really can beat the human fantasy… mindblowing…

Thank you everyone involved in this @ fractalforums, I think the things you all found is bigger than anyone of us can imagine!

-from http://www.fractalforums.com/index.php?action=gallery;sa=view;id=2759

There’s more images like this by Kraftwerk to be seen on his Deviant Art page, they all come from the internal details of this intriguing mandelbox structure:

I think the starry background has been added in, but it sure fits with this extraterrestrial space temple.  The coloring is really exceptional.  Kraftwerk has a real talent for that.  He’s made some of the best colored mandelbulbs I’ve ever seen.  He’s also using Jesse’s Mandelbulb 3D just like blob.  I find it quite interesting that both of them can use the same program and get equally good results and yet with such widely varying styles.  Fractal programs are bit like musical instruments: it’s not what you play but how you play it.

I can’t resist adding YouTube content to my postings.  So here’s a recording of the original Kraftwerk music group of “The Voice of Energy” which inspired fractal Kraftwerk’s title for this series of mandelbox images.  It’s in German.

7Up: The Un-Cola

What exactly does it mean to be un-Cola?  Cola drinks, like Coca-Cola, are dark-colored and contain caffeine.  The opposite would be light-colored without caffeine?  But both of them are sugary, carbonated drinks sold on the same shelf and dropping out of the same vending machine, or at least side by side vending machines (7Up is a product of Pepsico, Coke’s rival).

To those who like soft drinks and don’t like colas, then 7Up is perhaps very different.  Refreshingly different. But for those who are simply thirsty and don’t want to eat 10 teaspoons of sugar while trying to quench their thirst, 7Up and every other soft drink, including all the various members of the vast cola club, are all one thing:  cans of liquid candy.

Mosaics:  The Un-Fractal!

These mosaics, including the so-called mashups that are made of tiny images, are a kind of un-cola with respect to fractal art.  Their ingredients, like 7Up’s ingredients, are fundamentally different and yet seem to have all the same sweetness and fizz of regular fractals.

They look like fractals and from a purely visual standpoint, I enthusiastically declare them to be fractal art and insist they take their rightful place in that great vending machine –shining humming monolith of cold drink correct change worship– called fractal art.

And they’re cool to look at.  And maybe not so hard to make, either?  This one above I believe is a rendition of the screaming woman in the shower scene of Alfred Hitchcock’s Psycho.  There’s something called actionscript which does some really neat things like this.  Flash artists do similar things.  I have no idea how it works.  Wouldn’t it be funny if they used some type of fractal algorithm to scale the mosaic pieces?

You can view a whole bunch of them here on Village9991′s Mosaici page.  He’s Italian and lives in a small village in northern Italy.

The full-size (1800×1800) image is here and is worth a look.  The details in this mash-up are quite appealing, unlike most which get ugly when you move up close.

Jim Bumgardner is a Flickr master and has done some prominent things:

I’m a computer technologist / artist / composer in the Los Angeles area. I blog about my various projects at krazydad.com.

I’ve done a lot of mosaic art using the Flickr APIs, and co-authored Flickr Hacks, from O’Reilly, with Paul Bausch.

I’m a little obsessed with circles, radial symmetry and mechanical instruments.

* * * * * * * * * * * * * *
I work amongst an awesome collective of nerd/hipsters at Topspin in Santa Monica.

I did some mosaic posters for squared circle, and a day in the life, here on Flickr:

[see Giant Peach image above]

* * * * * * * * * * * * * *
One of the first things I did on Flickr was to make a number of fun-to-use Flickr Colr Pickrs. Check ‘em out!

I also made the world’s first Flickr Chia Pet, an experiment in collaborative defacement.

- From Jim’s Flickr profile page

I made something similar once, using a photoshop filter called Mosaic Toolkit by Lance Otis.  Over here.

Whaddaya know?  It’s the same guy as made the first one!  Well, I guess he’s got some sort of program to make these with because it would take a lot of work to draw these things even with a computer drawing program.

The woman, in case you don’t recognize her, is a detail from some very famous painting.  But here her image is made up of all the senseless words that people in art galleries have spoken while viewing the painting.  Individually, the words are gibberish and without any meaning.  But together they “speak” her image in a new but equally appealing way.  Some of the smallest comments are crucial details.  The other deep message in this image is: if you’ve got enough fonts installed on your computer you can do anything!

Time for another one:

Well hit my avatar with a digital two by four.  Same guy again.

He says it’s from a Pucca cartoon: YouTube Link.

The image has changed: it’s full of details that have their own (short) story to tell.

After watching a Pucca cartoon I now see the image differently.  I can clearly make out the two Pucca cartoon characters.  Nevertheless, the graphical effect is what makes this image interesting for me.  Those of you who are fans of the Pucca People you might feel differently.  Which is the greater art?

Blogging: The Un-Writing

I never intended to focus on the mosaic images of just one artist.  Incidentally, the way I review these things is a multi-step process and details like names often get temporarily lost in the shuffle.  First I wander around the internet and when I come upon an interesting image I bookmark the page.  This stores the link to the original (obviously) along with the image and any references to a title and author’s name.  Later on when I’m thinking of writing about something I go back to these collected bookmarks and I open up 10 or so from a single sub-folder bearing some (at the time) relevant name.  The folder names are often just dates like “June” or “May” or “3D”.  Digital art in general and fractal art as well is such an eclectic medium that meaningful sub-categories are hard to come up with.  And author names quite often aren’t the common ingredient in a particular graphical theme.

But sometimes they are. For me it’s all about art and not artists.  But you have to include the author’s name if for no other reason than readers want to know who made it.  Sometimes there are legal reasons such as attribution requirements.  Artists are less important in fractal art because individual accomplishment is more about the style of pushing buttons and operating the machine than it is about actually interacting with the canvas in the intimate way that painters do.  If you do what they did then you’ll “make” what they made.

Clearly, no one makes them like Village9991 does!

Fractal America

I’ve been looking at some mash-ups lately on Flickr ….and I was browsing around on Samuel Monnier’s site ….and July 4th, Independence Day in the States is coming up, …which is similar to Canada’s own national holiday on July 1st called Canada Day … I thought, “America Day” …and here’s two images of that great icon of America, the American Flag …and they’re both fractal, sort of …here’s Fractal America …the deeper you look, the more you see ...how close can you get?

Click on either one to see a larger version with much more detail.  Samuel Monnier’s image leads to a page where you can view the image in enormous detail.  He uses a special flash applet that allows you to practically explore the image to the same degree you would be able to if you were viewing it in the original fractal program (Ultra Fractal) that made it.  If you haven’t seen one of these before, it’s well worth a look.

Can the image of a national flag (especially the American flag) be purely something to look at and not have political overtones?

No.  Absolutely not.   And why is that?

Because it’s a symbol.  Our minds just refuse to look at it as if we’d never seen it before.

In social situations, if you want to avoid controversy, “don’t talk about religion or politics”.  But the American flag is both  politics and religion to many people –and not just the Americans.

In Canada (where I live) you will probably hear much more said about Americans and America than you will in America and among Americans.  Canadians are funny that way.  And so is much of the world.  No one see America (and Americans) quite like foreigners do.  And no one seems to talk about them as much as foreigners do.  Canadians, however, see America in a more powerful way because we are both foreigners and yet, in many ways, very american ourselves.  I won’t get into it right now because it’s too convoluted and confusing, but suffice it to say that Canadians embrace America with one hand while at the same time trying to get in a punch with the other.  It’s very hypocrital and juvenile and, I’ll come right out and say it: it’s very colonial.  Colonial-minded peoples are afraid of independence –they think they’re going to lose something.  Americans, on the other hand, enthusiastically fought for independence –because they thought they would be gaining something.

And there, in a nutshell, is the difference between Canadians and Americans.  Canadians like to complain about the government and you can’t do that when you’re independent because you’re only complaining about yourself.  Americans like to fix the government and to do that you need independence and self-government.  America wrote it’s own constitution.  Canada was content to let the British Parliament do it for them.  As a Canadian I’ve always found it surprising that my fellow Canadians don’t seem to see this as a huge national embarrassment:  Canada is an act of British Parliament. America was a reformation of the acts of British Parliament (“new and improved”).

See?  Already things have gotten political.  I’m so glad that art doesn’t have to be that way.  Let’s talk about art instead.

Samuel Monnier says that fractal art doesn’t have to embrace social and political themes in order to be considered “serious art” and that if you browse through artworks of the past you’ll find many examples of good art in which these sorts of themes are not involved.  Maybe he didn’t say it exactly like that, but he’s right.  The works of Joan Miro and Paul Klee would be considered “serious art” and yet they (rarely) had any connection to what one would call social commentary.

Of course it would be a great compliment to fractal art if it also had some artwork that did engage in social commentary.  It’s not necessary (as Sam says) for fractal art to be earn the label, “serious”, but it would add another dimension to the genre.  And political themes can be quite engaging and thought provoking.

Back to the art:  Sam’s “pattern piling” version of the American flag is really without any sort of intended meaning (assuming that’s possible with the American flag).  It really is just an interesting, richly detailed, experiment with the geometric qualities that this flag possesses.  He does the same thing with the Swiss flag (Sam is from Switzerland) although the results aren’t quite as interesting because the Swiss flag’s elements are all right-angled and lack the variety that the stars of the American flag give to it.  And there’s an extra color in the American flag which in turn provides for more combinations and permutations when pattern piled.

Qthomasbower’s flag is, on the other hand, a deliberate attempt to provide social commentary:  A vast mosaic of many artworks forming (by overlaying an image of the flag) a diverse but united nation waving majestically in the wind.  I think the technique is easier than it looks.  Nevertheless the result is fascinating.  It really has the detailed and intricate wonder of an image made by the iterations of a fractal formula.

Qthomasbower has some more of these on his Flickr pages.  Unlike Monnier’s image, Q’s doesn’t look so hot when you zoom in.  It’s kind of like the “digital zoom” on a camera;  the picture just becomes chunkier and cruder as you move in.  I’m sure he’s not implying that the state of American art only looks good from a distance and when covered by the imprimatur of The Stars and Stripes.

I find these mash-ups of Q to be very interesting because of the detail and texturing they give to the image when viewed at large.  I think almost any sort of half-decent image would look fantastic when treated this way.  It gives a large-scale and massive appearance to the image because of the non-repeating and highly detailed texture all the individual image “tiles” contribute.  The mash-up contributes really only a texture layer, but the effect, as I’ve said, is very impressive.

So.  Is America a fractal?  Does it have self-similarity at many levels?  Do parts of it descend down to zero while others escape to infinity? And why does a Presidential election with only two candidates take so long to render?

FractalWorks: One Smooth Machine!

The first time I saw an image made in FractalWorks it was in the gallery section of Fractalforums.com.  I was impressed and yet, I couldn’t quite figure out why I was so impressed.  There wasn’t anything really special about it and yet there was something really special about it.  It was one of those “height field” fractals, a (somewhat old) trick to give flat fractals a 3D appearance.  They’re all over the place and have been for years, but this FractalWorks one was different: more polished and more stylish than I’ve ever seen.  It also seemed to have a slightly surreal and mysterious quality to it –a strange kind of silence.

A comment by Paul N. Lee, the veteran fractal archivist, lead me to Duncan Champney’s website and to the incredible discovery that not only had Duncan made other images like the first one I’d found, he also made the program, FractalWorks, that they were created with.

There’s a long tradition in fractal art of people performing the roles of both artist as well as programmer.  Duncan Champney joins that royal list and furthermore offers his excellent program free to anyone who wants to share his passion for exploring what his super fractal machine can do.  But before you head off to download it I should mention that it’s for Macs only.

From what I’ve seen the program’s forte is 3D fractals of the height field, or geographical terrain,  “relief” -variety.  However, as simple and plain as that might sound in these modern days of Mandelbulbs and Mandelboxes, FractalWorks does this one thing very, very well.  These sorts of old-style 3D fractals made in other programs can be rather kitschy to look at, but FractalWorks manages to achieve a quantum leap in rendering quality that gives this old technique a new and vibrant appeal.  But of course as with almost any kind of fractal program, it still requires an artistic eye and the relentless persistence that only an enthusiastic explorer can possess to produce really good work with it.

Ordinarily I’d just shrug off stuff like this as eye candy but FractalWorks has elevated this simple type of fractal to a new level of sophistication.  There’s something fresh and different here.  Like I said when describing my first encounter, there’s something special and captivating about these FractalWorks works.  Some have a fairy tale look to them and others suggest a landscape that is much more surreal and haunted.  Don’t let the fruity, frosty renderings fool you; there’s more to some of these FractalWorks images than mere graphical sweetness.

Duncan Champney wrote the program and started up a Flickr group to get people interested in it as well as to offer advice and encouragement (I’m just guessing).  Although Duncan produces some of the best images made in FractalWorks, I discovered from the Flickr group someone who also makes work that is equally good: schimkent! I think the proof of a really great program is in what the users of it can do and not just the super results the author can get with it.  Shimkent (and others) have shown that Duncan has created a very capable and creative fractal art tool in FractalWorks.  Even if it is only for those Starbuck sipping, sophisticated Apple computer users…  They ought to have at least one good fractal program, shouldn’t they?

Schimkent: I think his real name is Kent Schimke (hence, the clever screen name –schimke-nt).  Kent’s LinkedIn profile says that he is “…helping a developer create a fractal generating program called FractalWorks for macintosh computers.”  I think it’s pretty safe to say he’s the guy.

Kent’s got a really good eye for color and also seems to have a good grasp of what makes for a good 3D FractalWorks scene.  Both he and Duncan have made some very eye catching and interesting images.  I would never have thought such a simple 3D height field program could produce such a wide range of creative works but I guess, as Kent says, “You just don’t know what you can’t do.”  Well,  Kent seems to have excelled in pushing FractalWorks’ envelope and taking us to new places.

In addition to his own Flickr gallery, Kent has also recently had a wall calendar featuring some of his FractalWorks images published by Browntrout entitled, Chaos Fabulous Fractals 2010.  This is not the Cafepress, self-publishing, print on demand type of thing (the one at a time whenever someone buys one), but rather the traditional editor/publisher/press-run type of publishing.

FractalWorks was released a couple years ago and since then it’s been upgraded a few times.  The most recent upgrade was just recently, May 4, 2010.  I’m sure the reason for such continuous development has been the impressive results users have achieved with the program.  That’s what usually drives fractal program development.  As the Flickr group message says:

FractalWorks is a free, high performance fractal renderer for Macintosh computers.
You can download fractalworks and try it yourself at the FractalWorks download site.

04 May 2010: Version 0.6.2 has expired. I just uploaded a new version, version 0.6.3 to the link above. Please upgrade to the new version.

-from the Flickr Group, FractalWorks site

I majored in Geography back in my university days and I think one of the things that drew me to that subject was all the imagery that one ends up studying, particularly the Remote Sensing images.  Perhaps part of the appeal that these FractalWorks images has for me is their similarity to maps and especially aerial photographs, something which the Wikipedia defines as “the taking of photographs of the ground from an elevated position“.

Another legacy of my geography days was the slowly developed ability to view stereo pairs of aerial photographs without the special lenses that make it easier for your eyes to perceive the 3D effect.  In digital art circles this special 3D imagery seems to be called “cross-eyed” stereogram.  I take it from this stereogram set posted on Duncan’s site, that FractalWorks is able to produce the paired images that produce this three dimensional illusion.  Here’s another also made in FractalWorks but slightly different in that you need red-cyan 3D glasses to view it (the old-style 3D movie glasses).  And here’s an even better one.  Wait!  This one too!  Go out right now and buy a pair of red-cyan 3D glasses so you can see this one!!!! (try the high res version on Flickr for an even biiiiiiger thrill).

FractalWorks produces a kind of high-quality imaginary aerial landscape.  Of course, that was always the intent I believe of the height field effect in fractal programs.  It’s just that FractalWorks has come along and achieved much better results than any other program that creates these kinds of fractal images, at least of all the ones that I’ve seen so far.  Although I’m sure Ultra Fractal or Chaos Pro could be programmed to produce similar smooth and richly colored images like this, no one seems to have attempted it yet (although there have been good examples of a mild form of 3D relief imagery created with them already).

Well, three cheers for Duncan Champney for making this Mount Everest Machine of fractal programs and taking us right up to the top of it along with him.  And to Kent Schimke, his agile sherpa for showing us how great the views can be.

Well, I could go on and on doing this.  These FractalWorks images are really something.  Too bad I don’t have a Mac.  Oh well, we can still look at the results.  You can browse the entire Flickr group at this link.  And should you happen to own a Mac, why not download the free program and try it out while you’re sipping your Starbucks coffee and looking as stylish and hip as Mac folks always do?

Fractal Art: No Money

I want to talk about the money in fractal art.

Where in the fractal world is there any sort of commercial success?  I don’t mean someone making some trivial amount of money, I mean someone making enough money to, as they say, quit your day job, kind of money.

Of all the artists, programmers, publishers, online instructors and other types of individuals in the fractal world, who would you say would be the most likely to be making some serious amount of money?

My first guess would be Ultra Fractal author, Frederik Slijkerman.  Ultra Fractal currently sells for $69 US for the standard edition and $129 US for the full featured, animation edition.  It’s a very popular fractal program and has been for ten years or so and is an ongoing concern as they say in business circles.  But has it made Frederik so rich that he’s moved into a castle and spends most of his time in his counting house counting all his money?

I don’t think so.  As far as I can tell, Frederik spends most of his working time at a regular (non-fractal) programming job.  (His Linked-in profile) I’m sure he’s making something off his sales of Ultra Fractal, but even if there were 500 paid-up users of UF5, and I think that’s a gross overestimation, that works out to about $35,000 US.  But put that in “earning a living” terms and it’s not much of paycheck compared to a regular job.

So, Frederick, of all people in the fractal art world who I would guess to be in a commercially viable position is probably making more money at his day-job than at his “fractal-job”.

I wrote a post last year entitled Is The Name Of Our Hero Benoit Mandelbrot Being Used To Market Ultra Fractal?.  But now I’d say that even if anyone ever had the idea of attempting to promote UF via this contest (and why would anyone think that?) that now it’s obviously a waste of time.  There simply are not enough users of fractal art software to generate even a modest income on an ongoing basis.  In short, I think Frederik’s motives in creating and selling UF are more personal than commercial.  I’ll bet he could make much more money with the time he spends developing UF by putting it to use on projects of a purely commercial and straightforward business nature (i.e. his day-job).  The fractal art world would have to change considerably, such as grow significantly in size and become much more trendy for this to be any different in the future.  And who’s to say most of those newcomers wouldn’t opt for the freeware program ChaosPro?

“More personal than commercial“.  I think this sums up all the rest of the fractal world from a money-making perspective.  But let’s look at online instruction anyhow, which, like UF,  is something that has had ties to the Benoit Mandelbrot Fractal Art contests via the judging panel.

No, there’s not much money there either!  Courses were about $25 US for a ten week course (two and a half months) and twice that for double semester courses.  Assuming you were a very keen instructor and you taught four course semesters a year and had a full class each time (not likely) what great pile of cash would you be rolling in at the end of the year?  Ten students a course, for instance, four times a year, and you (the instructor) get what?  Well, you wouldn’t get the whole $25 tuition, you’d have to split some of it with the online school who have their own administrative expenses to cover (and they want to get rich too, right?).  How about you get $20 per student at 10 students per semester and four semesters a year?  That would be (a whopping) $800 US per year.

Of course, if you’re trying to cover the rent  and buy groceries (you can’t get rich if you die on the way) then you might consider teaching more than one course.  Say you managed to teach 3 per semester.  3 x 800 is $2,400 US per year.  This is beginning to sound like a Get Poor Quick Scheme.  If money’s an issue then you need another job or you’d better just stay with a day-job.

Not surprisingly, none of the current or former judges of the Benoit Mandelbrot Fractal Art Contest are teaching online courses anymore.  Did they make too much money and decide to retire?  I don’t think so.  Their interest was, again, “more personal than commercial”.  I suspect they simply wanted to explore the option of teaching UF skills in an online environment.  Sure, there’s some money to be made, but it’s a token amount which might be some compensation for the instructor’s efforts but not a serious way to make a living or elevate one’s standard of living.  Would such a fractal-job income mean anything if you were applying for a mortgage? or a business loan?  Or how about bragging rights at a cocktail party?  “Hey, that’s nothing, man!  I’m a professional online fractal instructor and I made eight hundred bucks last year!”

Now how about selling artwork?  That ought to be worth something.  Hey!  Isn’t that how Picasso and Warhol got rich?  Ironically, I think this is probably the least profitable enterprise in the fractal art world.  And why would I say that?

Well, for starters, fractal art, like all digital art, is not collectible.  You can’t buy an original fractal print like you can an original painting.  You could print a limited edition of images and then (honestly say) you’re destroying the digital files (image and parameter files) just as print-makers destroy the original printing plate for art prints they sell after printing a numbered series of prints.  Throw in your (really famous) autograph into the package and then charge a bundle.

But the big problem with fractal art is that there’s so much of it around and it’s so easy to make.  People can shop around and find similar stuff for sale cheaper or even make it themselves. Can’t do that with Picasso’s paintings or Warhol’s silkscreens.  And of course fractal art isn’t as popular and as critically acclaimed as such traditional artworks are.  There’s probably money to be made in selling prints or fractal art for illustration purposes (book-covers, magazines…), but again, it’s some money, not enough to live on much less get rich at.  Yes, I think we’re back to the “More personal than commercial” aspect to things.

Alright.  Now I come to my main point in all of this:  Issues in the fractal art world are not taken as seriously as they would be if there were commercial interests at stake.

For instance: nobody really cares how the Benoit Mandelbrot Fractal Art Contests are run because winning or losing is purely a (temporary) matter of online status and has no impact on art sales or any other fractal commercial enterprise in any really significant way.  Maybe a few more UF licenses get sold because of the publicity, but I doubt it has any significant effect on anyone’s personal wealth or lifestyle.  (Actually, there is very little publicity generated by the BMFAC, isn’t there?)

I’ve seen artists advertising images on their websites as “Winners” in the BMFAC, but the real commercial opportunity would be selling prints right at the exhibitions themselves or at least taking orders.  Despite the other failings of the BMFAC, they have succeeded wonderfully in preventing the contest from becoming commercialized.  They don’t even sell a simple $10 souvenir poster or  wall calendar.  They could easily do this online from the contest site as well as from a table at the exhibition (hey, who needs a table? just stand by the door and sell them like newspapers).

Yes, the fractal art world is almost ascetic in it’s attitude towards fractal art and community events like contests.  We’re all in it for the art or for other things that have never had any commercial value like the social scene.  I believe that will change if fractal art ever develops a serious commercial side to it.  Until then it’ll continue to have the casual atmosphere of a community art club where even the big names are involved for reasons that are “more personal than commercial.”

10 Fractals and a Movie

Have I mentioned what a great addition to the fractal world Fractalforums.com is?  As someone who likes to review exciting new things in fractal art it’s really made my job much easier.  Before, I used to wander around Flickr or check out links on the UF mailing list or just stumble on something while surfing around.  I’ll probably have to go back to that again sometime, but until then I’ve got this alien planet filled with fractal treasure to report and review on.

There’s been a lot of development in the area of 3D fractals and the results, as I’ve been saying lately, have been impressive.  But one can still create interesting 3D work with some of the older methods.  The Stone Path is a good example of one of the older 3D techniques called height field (or something) and gives the impression of perspective though a special rendering trick.  These sorts of images aren’t usually very interesting, but this one by the username, Duncan C is a tasteful combination of subtle coloring and a well chosen perspective.  It’s not a marvel of cutting edge fractal rendering, but that makes it even more of an accomplishment because Duncan C is using well established techniques to produce an image that is equal to the others in it’s overall impression.

Buddhi seems to have created his own unique style of fractals in these smudgy, glowing 3D creations.  If you look carefully you’ll see lines on the x or y or z or whatever axes.  It’s a nice, technical, lab-diagram, touch in an image with such strong artistic style.  I reviewed one of these types of images before.  They’re really stylish and not like anything else I’ve seen.

Here’s an interesting Mandelbox by Dave Makin created in Ultra Fractal and titled New Rome detail.  The name I’m sure comes from the similarity the image shares with the ruins of the Colosseum in Rome.  The three dimensional details in this, and the excellent coloring which makes them stand out and look like such a carefully constructed and ornamented building is what caught my eye in this one.  It’s got amazing photorealism and shows how vivid and tangible these sorts of 3D fractals can be.

Elephant Canyon by bib, is another example of the older 3D style –or at least what appears to be the more traditional 3D style in fractals.  I think this is actually a “slice” of a Mandelbulb.  The contrast between the smooth, golden plain of the slice and the rough, craggy cliff of the edges is what gives this image its effect.  To me it almost suggests something about fractals themselves; that one often discovers things by accidentally falling off the edge or by traversing some huge empty plain and discovering at the horizon an abyss filled with rich and limitless detail.  This image was actually posted in a thread, Re: Problem replicating Mandelbulb power 2 and intended to be merely an additional illustration of the problem.  This comment by bib, accompanied his posting of the image: “Yes it’s always difficult to properly render the power 2, there too many chaotic shapes and calculation artifacts. When I saw this post I wanted to try again, so I did this image called “Elephant Canyon”. Nothing very original, but I like it “

Frozen in space. That’s what I think when I look at this one.  Another by Buddhi and having the same touch of the schematic style to it.  There’s an interesting structure formed by the repeating “bits” that form in a line off the major “pieces”.  Although this one is relatively monotone (one color), the lighting and surface texture effects are actually enhanced by the simple coloring.  That’s what makes art such a strange bird to capture and study: sometimes simpler things have a more powerful effect and sometimes they’re just simple.  The central core of the main object, back in the dark area, has an almost paint brushed appearance.  I guess that dark shadowed area is what draws our eye into it, but who can really say?  Trying to explain what makes an image impressive can often be futile as well as not being terribly exciting to read.

I guess it wouldn’t be called Mandelbox castle if it wasn’t a Mandelbox.  Once again the title really catches the essential quality of the image.  I particularly like how the moonlight (it’s nighttime) shines on the floor under the arch in the area to the right of the center.  If you’ve ever played Prince of Persia: Sands of Time (video game) then you’ll probably immediately think of the part of the game where the Prince had to walk along the tops of stone walls, fight big birds and then get into the room above the gate where the gate opening mechanism was.  Or others.  There were so many nighttime scenes in that game featuring different parts of an Indian castle.  Maybe game developers will pick up on the Mandelbox and produce a game that actually takes place inside one.  You could change the castle just by starting the game with a new set of parameters.

A pretty unusual color palette in this one by Jesse entitled Teeth but it works really well.  I would never have thought florescent yellows and greens could look so natural.  This is the “S2 cube”, which I assume is a variety of the Mandelbox.  Reminds me of a man-made planet in a sci-fi story.  Here’s another one with the same coloring and looking just as natural and appealing too.  Jesse seems to make some of the most unusual and offbeat versions of these 3D fractals.  He’s obviously experimenting with more than just the coloring, although he’s done a great job just with that alone.

This is another by Jesse taken from his Supercubes gallery section on Fractalforums.com.  Have you ever seen such a freaky fractal and with so much bizarre and yet carefully constructed detail?  They’re like egg cannisters and they grow on the sides of the bigger egg things in strange patterns and all over the place too.  I remember back in my early days of using Sterlingware, I was zooming into a fractal that seemed to be made of red velvet curtains.  The “curtains” were quite intriguing but then while zooming in further I discovered shiny eggs growing under them.  All this makes it rather difficult to define what a fractal is or to explain to someone what fractal graphics look like.  There’s just too many freaky things to be found.  There’s fractals and then there’s “freak-tals“.

Xenodream has not been left out of the 3D fractal craze here.  This one is by xenodreambuie and had the label, Triplex Z=rcosphi Julias.  I think a better title would be Catalog of the Fractal Brains.  They’re all very rich in well rendered, three dimensional details and colored well even though I think the method is a fairly basic one.  The numbers are in there for technical reference of course, but I think they add a nice artistic touch as well.  This would make a very appealing wall poster.  I’ll bet if you showed this image to people and asked them what kind of textbook it came from they’d all guess it was Biology and not Math.

Arch detail by Tglad (2010 Nobel Prize Winner, incidently) is interesting for the, well, details of this arch it shows…  Another great title.  See how the section in the lower right appears to be eroded away?  That’s all algorithmic.  The main arch structure off center to the left is interesting too with its floating triangle center.  The coloring gives it all the impression of being carved from wood or some sort of soft stone.  There’s always something new to see in the Mandelbox.  I think it’s going to be a popular formula for some time.

I said 10 fractals and a movie and here’s the movie.  I forget how I stumbled on this one.  I think I saw it amongst the entries in the current Fractalforums.com contest in the animation section.  However I didn’t actually view it right away (that’s a problem with animation, you can’t just take a quick glance at it).  I only looked at it for the first time while visiting subblue’s website (subblue.com).  For those of you who often skip videos if you don’t happen to like the title picture, this video features a very good soundtrack which straddles the categories of sound effects and slow paced instrumental music.  Also featured is some of subblue’s special, black and white, polished steel renderings of the Mandelbulb.  It’s some of the best video rendering of the Mandelbulb actually.  Anyhow, with good graphics and a smooth professional soundtrack, it’s worth taking a look at.

The music is actually not by subblue but by The Formula.  Here’s a link to subblue’s blog which has a larger version of the video and has a bit more information as well as a very long string of glowing comments.

The Formula from subBlue on Vimeo.

Well, there you go; 10 fractals and a movie.  And it didn’t even cost you 10cents like Tales of the Unexpected comic books did fifty years ago.  The internet is just a such a great and wonderful thing.  Let’s hope it stays that way.

A Knighthood for Knighty

I continue to dig through the treasure trove of fractal visions over at Fractalforums.com.  In fact, lately it seems to me that the center of the fractal world has shifted to Fractalforums.com.  It’s become the Paris/Milan/New York/London/Tokyo for new fractal fashions.  Is there anything new and exciting in the fractal world right now that doesn’t have its roots in Fractalforums.com?

Although the obvious sequence of parameter adjustments is what this image is all about, and I think it was posted merely as an illustration in a Fractalforums.com thread on Kaleidoscopic (escape-time) IFS fractals (KIFS, for short), the color palette really makes this image much more than merely functional.  I think Knighty realized this too since he’s used this same palette quite a bit.  It’s one of the best I’ve seen on this new fractal frontier.

[Knighty starts this new topic, May 1st, 2010]

Hello,
Here are some renderings of a class of fractals which I call “Kaleidoscopic IFS”. There is a big variations of shapes one can get with this method.
I began with this algorithm to get DE for symmetric Sierpinski tetrahedron:

[From Fractalforums.com, Kaleidoscopic (escape time) IFS]

Just like the early Mandelbox renderings by Tglad, the KIFS made by Knighty showed real graphical promise right from the first batch posted.  Here’s one that of the first few that received quite a bit of praise:

[Knighty responds to the initial comments:]

There are many other known fractals that may appear from nowhere. I’ve already met the Koch curve, cantor dust and others I don’t know the name. The variation of possible shapes, from geometric figures to organic forms, still amazes me. The possibilities are infinite  , not only by changing the parameters but also by changing the algorithm.

What I’ve described in the O.P. is actually what I’ve explored so far. The main ingredients are the folding and the stretching, that is, kneading the space . Then add some salt and spice. Seriously! In the case of this class of fractals, folding are done about planes and stretching is an homothety. The rotations may be the salt and spice. I realize now that one can insert as many rotations between the foldings. In principle other transformations than a rotation can be used (but I may be wrong). The nice thing with rotation (and other orthonormal transformations) is that the distance estimation remains very simple and the generated distance field is continuous. I guess because they don’t add stretching.

I think the kneading process is what is done to generate escape time fractals in general… but this is a little bit off topic. I’ll start another thread.

PS: Most ideas behind these fractals were found in this forum.

[From Fractalforums.com, Kaleidoscopic (escape time) IFS]

If you read the forum thread you’ll see that many other people get involved.  In fact, according to Knighty’s remark, “PS: Most ideas behind these fractals were found in this forum” there’s been a lot of collaboration going on already.  The sort of group exchange of code and ideas which seems to be the hallmark on Fractalforums.com immediately starts to take place.  In addition to the regular 3D fractal enthusiasts, the venerable Jos Leys (of 3D Kleinian fame) joins in as well.  Only a truly great knight would have so many squires and inspire so many others to join in his exploits.  Is there an Order of Sierpinski?  An iterated knighthood?

Subblue charges forth with these surprisingly monochromatic but still very exciting renderings:

With more sublime renderings Knighty produced this family portrait of the Royal (3D)House of Sierpinski:

There’s more.  In fact, you ought to just go over to the gallery section of Fractalforums.com and view Knighty’s Kaleidoscopic IFS section.  But here’s two of the more interesting ones so you don’t miss them:

Pagode is an interesting construction.  Although a higher resolution rendering would probably be even more impresssive, even this small version shows the sort of intricately detailed and vividly rendered imagery that Knighty has discovered with his KIFS fractals.  Like the Mandelbox, these KIFS are very creative in that they seem to have an almost endless number of variations depending on how one folds and twists the characteristics of the formula.

You know, I suppose if you’d seen this Pandora_seashell lying on the lawn in your backyard you might just think it was a rotting leaf.  But sometimes the “art” is in looking more closely at something that we’d otherwise, uh… step on.  Art is on the boot of the beholder.  Math is a very natural thing and for that reason I think it’s easy to make assumptions about mathematical, or algorithmic, imagery.  Such as assuming that it’s repetitive or predictable.  But I think Knighty’s recent discovery of these Kaleidoscopic IFS fractals shows that there’s still plenty of things to be discovered in this area (it only started at the beginning of this month, May 1st, 2010).  Maybe there’s no end to all of this and this is merely the beginning?

Well, it’s all happening over at Fractalforums.com, so stay tuned to that forum if you want to catch the next great event in the fractal world.  Perhaps some day all the rest of the fractal kingdom will be mere footnotes to Fractalforums.com.  While Knighty and his other fellow members of the Round Table feast on roast boar and crash their flagons together in an endless round of toasts and heroic tales of fractal exploits.