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.

It's more than a forum, it's a wild alien planet of the UNEXPECTED (image from Coverbrowser.com)

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.

Stone Path by Duncan C, 2010

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.

Trigonometric 3D Mandelbrot by Buddhi, 2010

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.

New Rome detail by Dave Makin, 2010

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 smiley

Elephant Canyon by bib, 2010

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.

Hypercomplex Julia by Buddhi, 2010

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.

Mandelbox castle by bib, 2010

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.

Teeth, by Jesse, 2010

Teeth by Jesse, 2010

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“.

Birth by Jesse, 2010

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.

Triplex Z=rcosphi Julias by xenodreambuie, 2010

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.

arch detail by Tglad, 2010

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?

Sequence, by Knighty 2010

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:

"last picture" by Knighty, 2010

[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  wink, 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 grin. 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. wink

[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:

untitled by subblue, 2010

untitled by subblue, 2010

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

.

Tetrahedra-Sierpinski-family by Knighty, 2010

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, by Knighty, 2010

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.

Pandora_seashell by Knighty, 2010

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.

Privately Owned Algorithms?

Mine -- down to the integer!!

It’s mine!!  All mine!!

[Image seen on nikadon.com.]

Can one patent abstract ideas?  Or claim equations as intellectual property?

The U.S. Supreme Court will likely make a decision in the near future concerning the constitutional scope of patents.  The decision could have profound implications pertaining to the legality of free software — and possibly have ramifications for fractal software, fractal programmers, and fractal artists.

David Bollier, writing in OntheCommons.org, lays out the dimensions of the court case:

At the heart of the case known as Bilski v. Kappos is a “business method patent” application that sought to obtain a patent for a method of managing the risk of bad weather through commodities trading. Bilski did not build any invention or device, as traditional patents have required; he came up with a method of doing business that orchestrates human knowledge and interactions, for which he believes he deserves a patent.

But this is the passage (and question) that caught my eye and caused me to reflect on possible ripple effects in the fractal art community:

But should the government be in the business of granting legally protecting monopolies on abstract ideas such as “business methods” and mathematical algorithms? The outcome of the case is being watched closely by the free software community because it could negatively affect the future of collaboratively developed code.

Can algorithms be privately owned?  Maybe — at least that is what some legal precedents seem to suggest.  Bollier clarifies:

Patents are given out so freely by the U.S. Patent and Trademark Office that companies have the legal rights to all sorts of abstract ideas, some of which may be embedded in software. “One-click shopping” was one of the earliest, most infamous business method patents granted. “If you’re selling online, at the most recent count there are 4,319 patents you could be violating,” said David E. Martin, chief executive of M-Cam Inc., an Arlington, Va.-based risk-management firm specializing in patents.

A key issue in the Bilski case is the appropriateness of granting patents for software and other sorts of collaboratively produced Internet works. It once made sense to grant patent monopolies over inventions developed by individuals or companies, but now that the Internet makes online collaboration so powerful and efficient, should anyone be allowed to privatize collectively generated knowledge and then charge premiums for it?

I predict a massive mess in Fractaldom if the court ruling codifies algorithms as deserving of patentability.  Imagine the chaos (no pun intended) if Ultra Fractal‘s poobah-programmers decided to patent their formulas, or even parts of them.  UF, which relies heavily on user-based formulas and openly encourages tweaking, not to mention its ability to combine lots of soon-to-be patentable private property into layers, might become nearly unusable since any image made with UF could be stuffed with patent violations.

In fact, in a worse case scenario, the creative forces behind Ultra Fractal, who did a bit of liberal borrowing when initially creating the program, might find themselves facing some retroactive monetary compensation to some of these folks:

One for all -- and none for us...

We gave freely of ourselves so that UF’s author and select courtesans could prosper.

[Image seen on AliceKelley.com.]

Currently, “pure knowledge” like algorithms is not patentable. However, if the high court rules in favor of more stringent patent restrictions, the result could be especially devastating for open source programming.  Would innovation still occur when some aggregated components suddenly become patented?

And, artists, what about all of “your” images made with free fractal software?  If the author of such software can soon own many of the formulas you used, will you have to pay a kind of licensing fee to display those images — or else be forced to remove them from any public sphere?

For whatever it’s worth, according to court reporters, the SCOTUS justices generally did not warm to the idea of broadening the scope of patents.  According to The Prior Art:

Across the board, the justices indicated a deep skepticism toward the invention described in the patent application at issue.

[…]

Some of the justices went even further — expressing both a fair amount of disdain for the idea of granting broad “method” patents and a concern that ruling in favor of the petitioners would lead to patent grants on fundamental ways of conducting business or organizing human behavior.

Still, even if the U.S. high court rules against such an amplified view of patents, courts elsewhere in the world might begin to weigh in on such matters.

I sense this case could have far-flung knottiness for most of us, but I admit my own shortcomings here.  I am not an attorney, nor am I well versed in legal matters.  Subsequently, I’d welcome hearing from any of OT’s readers who might be able to shed more light on what is and is not at stake here.

~/~

If you’re interested, you can view an admittedly subjective thirty-minute video discussing the origins of software patents and their detrimental effects.  It is entitled Patently Absurd: How Software Patents Broke the System.  It was made by filmmaker Luca Lucarini and financed by the Free Software Foundation.

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Fractals Don’t Have to be Fractals

I often find myself preoccupied with justifying fractals (and other types of computational imagery) as art; trying to link fractals with the larger stream of visual art that has flowed and enriched (and provoked) our culture since pre-history.  I don’t know why it nags me so much.  I don’t think most fractalists are very concerned with what outsiders think about fractals or how they may label them.  Maybe that’s a more sensible attitude to have than the one I have which seems to keep wanting to write an Art Manifesto, Bill of Rights or a Declaration of Independence for fractals.

My latest inspiration to write a fractal Magna Carta occurred when I saw this Mandelbox image by Pauldelbrot (Paul Derbyshire, I think) posted at Fractalforums.com.

Escher's Eiffel by Pauldelbrot, 2010

It’s weird, but I hear things when I look at this image.  I don’t really mean I hear audible sounds (that’s nuts!), but the image suggests to me the sound of icebergs bumping against each other underwater:  Great, massive objects in motion.

Or mountains.  Does this image not make you look up and see the distant, towering faces of whatever that smooth-sided thing is?  Is there a basement of the mountains, where the roots and feet of them are exposed and we see where they come from and what they stand on?

Yes, Pauldelbrot’s Mandelbox image here is every bit as expressive as a great Ansel Adams photograph or one of the Group of Seven landscape painters whose impressionistic and semi-abstract style displayed the raw, muscular beauty of the Canadian wilderness.

A few disjointed thoughts about fractals and art:

  • The images speak for themselves
  • They are what you see (and hear)
  • It doesn’t matter how they were made
  • They’re as much an art form as Paul Klee’s work is
  • They express themselves in a language of shape, form, color and pattern
  • They have a symbolic kind of expression
  • Good art is the stuff you keep coming back to look at
  • Design and ornamentation is visual music
  • Serious art is any kind of art you take seriously
  • Fractals are captured, not painted
  • Fractals are an abstract and imaginary type of imagery like Abstract Expressionism or Surrealism
  • Fractals are an interesting world just to explore; you don’t have to take your camera with you
  • Fractals don’t have to be fractals, they can be landscapes, sacred smudges or forbidden cities

Here’s two more by Pauldelbrot.

Moss by Pauldelbrot, 2010

The moss-covered stone ruins are a good example of the imaginary kind of themes that fractals seem to instinctively display.  It looks realistic, but the strange patterns in the stones are unreal.  Can you spot two cavities or spaces in the stones that look the same?  This shows the enormous creativity of the Mandelbox fractal: everywhere you look there’s something new.  That’s what creativity is all about: new things.

Trusses by Pauldelbrot, 2010

How about: Grendel trashes the mead hall? Amazingly photographic.  Note the glinting reflection of light on the truss in the foreground.  Would a professionally taken photograph of a ruined temple be clearer or more vivid than this?  There’s great imagination at work in the construction of these trusses and it all comes from a fractal formula (and an enormous amount of computing).  There’s a touch of the surreal in this image; its as if it was the illustration to one of those H.P. Lovecraft stories about million-year-old, pre-human temples of the cosmic elders.

Well, I haven’t finished my odyssey, but Pauldelbrot’s recent Mandelbox images posted to Fractalforums.com have certainly moved me on to the next island.  Actually, I don’t care if a voyage like this never ends.

2010 Nobel Prize for Fractal Art

For his work in discovering the Mandelbox formula of 3-D fractals, the winner is Tom Lowe, better known on Fractalforums.com as Tglad.

Now some might ask why Daniel White and the Mandelbulb Team weren’t this year’s Nobel recipients, but while the Mandelbulb discovery was truly the most exciting event in the fractal world this past year, and possibly the past two years, and has certainly received much more popular attention and interest, I felt the development of the Mandelbulb was an achievement of a more technical and scientific nature while the Mandelbox represents a development with a much greater impact and influence on fractals as an art form.

Paul Lee (Nahee_Enterprises on FF) recently made this remark here on Orbit Trap in a comment:

Yes, the Mandelbulb really became quite “famous” back in November, but the recent variation of the Mandelbox has added a lot more to the visual aspects on the current trend in fractal imagery. There are so many good examples to choose from that it is difficult to fully represent what can be done with the new set of programs and algorithms available.

There are so many examples because many others have noticed the potential of the Mandelbox formula and since these things have been so freely shared without restriction with other fractalists, the formula has been incorporated into a number of programs such as Krzysztof Marczak’s (Buddhi) Mandelbulber and Mandelbrot 3D by Jesse (I only know his screen name), both of which are freely available.  Furthermore, thanks to the help of veteran Ultra Fractal programmer, Dave Makin (alias David Makin on FF) the Mandelbox formula is available for UF as well.  In fact, I believe UF is what Tglad used for both his current and early renderings of the Mandelbox.

The Mandelbox didn’t exist until February of 2010, which means at his point it’s only been around for about three and a half months!  Like the the great Mandelbulb discovery, you can follow the development of the Mandelbox from it’s earliest form as an idea in Tglad’s head (inspired by a related group of 3D fractals) to it’s final incorporation in the three programs I just mentioned.  It all happened on Fractalforums.com and one can at least speculate that without Fractalforums.com and Christian Kleinhuis’ (Trifox) sponsorship and management of that online fractal forum, such advances in fractals may not have occured or would have been greatly hindered.  It’s also possible, I think, that the excitement and attention which the Mandelbulb event stirred up, also attracted and brought together the people who developed the Mandelbox.  I’m still reading through the archives of all these threads over at Fractalforums.com (and trying to keep the screen names straight) so I’m not as up to speed on these events as others who’ve been following them for longer may be (i.e. I could be wrong…).

Here’s the main thread about the Mandelbox entitled, Amazing Fractal.  It starts out, just like the Mandelbulb quest did, in a very simple and low-key way:

This is a new fractal that is member of the fractals described in http://www.fractalforums.com/3d-fractal-generation/continuous-conformal-mandelbrots/msg12464/#new

The formula is simple:

[ from Fractalforums.com ]

Even the very first examples of the Mandelbox were visually attractive.  Right away anyone can see the strong design qualities and rich variety to the Mandelbox.  Look closely and you’ll see very little of the self-similarity or repetition that most other fractals have.  This is a very un-fractal fractal, figuratively speaking.  Here are the first three posted by Tglad at Fractalforums.com on February 1st, 2010:

By Tom Lowe (Tglad) Feb. 1, 2010

By Tom Lowe (Tglad) Feb. 1, 2010

By Tom Lowe (Tglad) Feb. 1, 2010

Tglad has put together a small online gallery for the Mandelbox and it’s best for you to go there and read his explanations of the Mandelbox since the technical side of fractal art is not my forte.  One thing I can mention however is that the Mandelbox exhibits something which is a rather uncommon sight in fractals and that is a great amount of non-self-similarity.  This, of course, is what makes the Mandelbox so much more interesting (from an artistic perspective) than the famous Mandelbulb.  Tom has involved two features that I think I understand: Julia sets and Folding.  What it comes down to is that you don’t see the same shapes, forms and patterns everywhere in the Mandelbox just as you don’t see the same shapes and forms in every Julia set of the Mandelbrot formula.  Julia sets are one of the easiest ways to produce graphically appealing variations of the Mandelbrot set that’s part of the mix found in the Mandelbox.  The folding feature Tom has introduced just adds to the creative powers of the Mandelbox while at the same time maintaining it’s strong design qualities through rigorous and careful combinations of patterns (folded over on each other and rendered together).  How’s that for a non-technical description of the Mandelbox?

One other thing:  Like the Mandelbulb and probably all 3D fractals and other types of 3D graphics, the Mandelbox will make good use of all the processing and memory resources your computer has.  If you’ve been waiting for a good reason to upgrade you computer, this could be it.  But as you can see, even from these prototype images of the Mandelbox, the rich results make all the time and processing power worth it in the end.  Take a look at this internal exploration of a Mandelbox done by bib (Jeremie Brunet) which was based on a series of images posted by Tglad to FF.  I’m sure this took some time to make, but again, well worth the effort, I’d say.


Since that day in early February, 2010 there has been a lot of rendering variations of Tglad’s original formula but Tglad’s own work still ranks among the best that I’ve seen.  Although Fractalforums.com may not be, as Christian Kleinhuis (Trifox) himself stated in a comment here at Orbit Trap, a fractal art site but simply a fractal site with an associated image gallery, many of the images there have strong artistic qualities and fulfill the role of art as much as they do the role of illustrations embedded in their related discussion threads.  Tglad’s posted work is one of the best examples.  From his earliest examples of the Mandelbox formula to the one below, posted 2 months later, he’s demonstrated that in addition to his technical skills of a formula developer, he also possesses a real eye for art, particularly color and composition.

Helicopter Ride by Tom Lowe (Tglad), March 30, 2010 (click for full-size)

In closing I’d like to say that I think the Mandelbox and the other 3D fractal types have ushered in a new era of fractal imagery.  A lot of the older, 2D stuff looks pretty stale to me right now and I don’t think it’s a temporary feeling.  I noticed this particularly while browsing the Fractalforums.com gallery.  The old stuff looks even older to me now.  I’ll have to confess that over the last few years I’d become rather bored with fractal art in general.  The only thing that really interested me was my own work and that of Samuel Monnier’s “Pattern Piling” technique.  The Mandelbox and other 3D experiments on the Fractalforums.com site have changed all that for me.  Fractal art is exciting again and it’s because of these new algorithms and formulas and the great imagery they produce.

It’s more than just being “3D” instead of “2D”.  It’s not like all of a sudden the images are exciting because they’ve been enhanced with some new feature or gimmick.  What the 3D algorithms have added to fractal imagery is much more substantial than just another kind of enhancement.  What’s new and different are these fresh new designs, forms and shapes that the 3D algorithms generate that the old 2D algorithms couldn’t make.  Of course, ultimately, everything becomes a flat, 2D image on a computer screen (unless it’s a 3D stereo image set) and whether the depth and perspective in the image comes from a system based on 3D voxels or just 2D pixel rendering tricks (height-field; bump-map) it all has the same effect of giving fractal artists more tools for use in their creative pursuit of making fractal artwork.  To the fractal scientists however and the formula developers, these differences in the underlying mechanics have more meaning and subsequently attract more of their attention (i.e. not everyone pursues fractals for the same purpose).

It’s a fractal renaissance. And if I had to pin an award on just one of the many people who have played a role in bringing it about I’d choose Tom Lowe.  Or rather, I’d start with Tom Lowe.  I’ve got many more awards to give out, a Nobel prize is just the beginning.  I’ve also got a:  Knighthood; Oscar; Medal of Honor; Purple Heart; Court-Martial; ye olde forty minus one…  There’s more.  A lot more to come.

3-D Fractals: A Voyage to the Mandel-Worlds

I don’t know what happened, but all of a sudden there’s a new crop of 3-D fractals sprouting up and they’re seriously amazing.  I’ve seen 3-D fractals before but these Mandelbulb and Mandel-box things have taken 3-D to a whole new level of sophistication.  The best phrase I can think of to describe them is Majestic Panorama.  It’s like a glimpse of a new world and not merely a new rendering technique or formula.  There’s a depth and style to these types of 3-D images that I’ve only seen in photographs and oil paintings and never before in digital art.  I found them all in the Gallery section of Fractalforums.com, my latest re-discovery in fractal art.

Is it only eye-candy?  or 3-D video game backgrounds?  Or is it the start of a new genre of fractal landscape and panorama that began with programs like Terragen, Bryce and Xenodream but has only now reached a level of sophistication and creativity that sets it apart from everything else ?  It’s this kind of powerful algorithmic creativity that first got me interested in fractal art and then led me to look elsewhere as most fractal artists headed off down the dead end road of endless layering.   Yes, what a breath of fresh air these bold new 3-D things are –however you may like to label them.

One thing I should note:  Many of these images are snapshots of work in progress and early examples of newly developing rendering techniques.  They weren’t necessarily intended by their authors to be finished artwork for display or exhibition.  I’ve reviewed them here simply because I think they’re extremely interesting and worthy of greater attention and viewership.  Also, I’m not up on the technical side of the Mandelbulb and Mandelbox stuff because it’s very new to me.  I’m not even familiar with the software.  Hey, I just like looking at computer made pictures.  Here’s some cool ones…

mandelbrotbox-experiment-1 by ker2x (click to view in majestic panorama mode!)

— update: 05/12/2010: click here to view a much higher resolution version of ker2x’s mandelbrotbox-experiment-1

Like all of these images, you really have to view them fullsize which you can do by clicking on them.  This one really shows the freaky, sci-fi and particularly three-dimensional awe and wonder aspect to these types of images.  The landscape itself is intriguing but the hovering island (and copper/emerald color palette) makes this image simply monumental.  Also, the hazy, “aerial perspective” accomplished in the rendering makes this image look extremely polished and as carefully created as if it had been painted by hand in oil paints.

Retro Metal Cathedral 3 by MarkJayBee

Click it to check out the larger version at Fractalforums.com.  What makes the detail in images like this so spectacular I think is the depth and incredibly realistic lighting.  Although ray-traced images can be intensely realistic and almost “perfect” looking, they don’t have that “aerial-perspective”, that vast expanding background and distance that this images demonstrates so well.  This reminds me of something painted by the old masters like Raphael in his The School in Athens fresco.  Of course no 3-D fractal will have the expressive human figures and all those sorts of things that human painters depict, but they can like this one match the magnificent perspective and three dimensional design that Raphael’s setting and background has.  Actually, I think MarkJayBee’s image here is better in that respect.  Sorry, Mr. Raphael, but you just didn’t have the Mandelbulber program to help you back then.

before the rain, by Tglad

Doesn’t this have a certain Maxfield Parrish look to it?  I don’t know what all the programming and rendering tools were that went into this one, but the results are unlike anything I’ve ever seen before made digitally.  I don’t just mean the lighting and 3-D look, I mean the creativity in the image itself also.  This has the variety and unpredicability of a real, natural landscape.  It doesn’t have the repetitive look that most fractal formulas have.  There’s recursion here, but it’s not carbon-copy or of a purely repetitive nature like say, sierpinski objects have.  You could wander around in this small sample of landscape for ages and not have explored every detail.

Thing by knighty

Here’s a good closeup of the exquisite and wondrous detail that these 3-D “things” have.  Such things as this, although they look realistic enough, could never be made (gravity’s not a problem in the Mandel-Worlds like it is here) but if they could they would rival the sculpture and design of any human made temple or architectural wonder, at least from a design perspective.  Knighty chose a good title as the image speaks for itself and who could ever give this a fitting name?  I saw a lot of very intriguing architecture and 3-d works in the Star Wars second series of movies, but this kind of imagery exceeds that in quality and creativity.  And these “things” can be animated, too.

Aztec Farms by Timeroot

Here’s an even bigger version than the one you’ll find at the Fractalforums.com gallery.  You can clearly see by the “Evaluation Copy” watermarks that this image is fresh from the laboratory.  I’ve included it because, like all the others, it’s such a majestic panorama.  I was really stunned when I first stumbled on this one.  It’s got the level of detail that only electron microscope or satellite photos usally have.  The title is quite appropriate too as it does resemble a vast area of farmland in the desert like a kibbutz in Israel.  There’s so much variety and well rendered details in this one that I just had to include it even though it’s got all those watermarks on it.

The Golden Hour 1 by MarkJayBee

You can’t get a better example of perspective than this image.  This is like those Grand Canyon photographs that one sees in every travel magazine: you just want to dive into the picture and fly away.  Artists used to spend a lot of time and get paid good money for making spectacular scenes like this.  We’re really living in a golden age of art, or if you prefer, visual imagery.  We’re seeing things every day that most explorers and world travelers could never imagine or hope to visit.

entrance to the hole, by Tglad

Reminds me a bit of Dave Makin’s video tour of the inside of his golden sierpinski temple which I included in a previous posting on animation.  Again, look at the incredibly lifelike perspective shown in the mouth of the “hole”.  These images are so vividly rendered and yet also so full of rich algorithmic details.  The green, “tarnished bronze” coloring is a nice touch too and adds a subtle outline and resulting perspective to the image.  I keep expecting to see someone walk up to the balcony railing and begin to issue a royal proclamation.  This would make a nice model for rebuilding the Jedi Temple.

Bulbox3 by Jesse

This one really needs to be view full-sized to fully appreciate it.  What I find most impressive about this one is that although everything looks like it’s been roughly chopped out of stone, there is a precision and carefully laid out design that it all fits into.  Very intricate and yet having a primitive style to it at the same time.  Also, although the image has a reflective or mirror-image quality to it, if you look closely you’ll see that very few of the opposing and apparently “mirrored” structures are actually identical.  The plain background is a nice touch and shows off the rest of the image quite well.

Plastic Mandeltoy by MarkJayBee

The smooth plastic texture in this one is unique.  I find it gives the impression that the details have been exposed by chipping the plastic matrix away rather than being carved from it.  I guess it’s probably a simple image in some ways since it’s just a cube, but as with all these Mandelbox things, there is never anything simple about them.

Inside Tglad's Cube by buddhi

I think the best comparison one can make to an image like this is a fossilized plant.  I’ve seen plant fossils in museums and they have the same delicate detail and stone like qualities to them.  I take it that “Tglad’s Cube” is a formula made by Tglad.  Buddhi, the author of this image, also made the program that created it, Mandelbulber (just for Linux).  I tried it out on my ancient computer (P4 2.26 Ghz “single”-core) and it works perfectly although I wasn’t able to make anything approaching the cool stuff these folks I’ve reviewed here have.  You can see the sort of synergy that been developing over at Fractalforums.com with this 3-D fractal experimentation.

Exploring fractal planet by bib

You see here?  Everything these 3-D fractal programs generate is awesome.  Even this crevice in the side of  this larger (I’m guessing) Mandelbox planet is cool to look at.  It’s like the whole thing is one gigantic carefully carved piece of art.  And I’ll bet every cave and crevice like this one is different in some way or another.  Very nice coloring.  The texture looks genuinely rock-like and the darker tones gives a nice shadowing and relief to the imagery.  Nicely composed too.  And the shadowed area to the right of the center suggests there’s more to be explored if we wander in –unless of course something lives in there.

So there you have it.  For the first time in a long while there’s something I find that’s genuinely new and exciting in the fractal world.  I’ve got more to show you, but I thought I’d just focus on the Majestic Panorama genre for now.  In the meantime I suggest you check out the Gallery section yourself over at Fractalforums.com.  It’s a pretty good collection all on it’s own created by the contributions of the many forum participants that have gathered over there.  It’s not the usual sort of fractal gallery and I think you can see from what I’ve reviewed here that it’s got some really great works in it.

FractalForums.com Spring 2010 Competition

I found this email in my inbox just yesterday and quickly felt my fractal art commentary sap rising boldly in my branches.  Here, read it carefully and see if it has the same Spring-Time for Fractaland effect on you:

FractalForums.com Spring 2010 Fractal Art Competition Submission Period has Ended

The Entry Submissions time frame for the “FractalForums.com Spring 2010 Fractal Art Competition” has now ended.  This submission period set a new record for Member Activity on the FractalForums, with around 650.000 Page Views!!!

We would now like to enter the voting period, which will last until the end of May 2010.

We have a total of 130 entries to the three different competition sections.  And due to the large amount of entries, please take your time to review each of the submissions and give a reasonable vote for what you consider “best” images per category.

Only the Gallery votes count for the results.  So, no external embedded video Sites Rating system is taken into account.

The ranking will be as follows:
– highest average rating
( if tied for same position, then )
– most votes
( if tied again, then )
– sharing of winner placement

Again, we ask that you please take your time and review each category of the competition, the sections are as follows:

•  Mandel Brot  —  Only views of the standard z^2+c Mandelbrot set and Julia Sets where allowed, and this section has more than 47 spectacular entries:
http://www.fractalforums.com/index.php?action=gallery;cat=38

•  Fractal Fun  —  Contains computer generated fractal art of any kind.  This section was the most popular with more than 64 entries.
It is a vast mixture of state of the art Mandelbulb renderings and beautiful 2-D creations:
http://www.fractalforums.com/index.php?action=gallery;cat=37

•  Fractal Movies  —  For the first time in the Forums’ history, there was a movies/video section, with a total of 19 entries.
You will encounter interesting new locations of the Mandelbrot, plus amazing 3-D fly-bys and inside explorations. Enjoy a total of 40 Minutes of extraordinary Fractal pleasure:
http://www.fractalforums.com/index.php?action=gallery;cat=36

Voting Period will end on:
1.June 2010

Well the internet is a wild and wooly frontier place of lawlessness and I intend to judge this here contest right here!  But before I pull out my six-shooter to choose the winners (and scatter the losers), I’d like to ask the question, “What’s up with this FractalForums.com place?

It’s been around for a couple of years and that’s the strangest part of it.  Fractal forums and other community venues almost always fold up after the intoxication of the opening event wears off.  That’s about 3-6 months, I’d say.  That’s how it was for Orbit Trap’s campfire singalong days.

But FractalForums.com is still singing and the campfire isn’t going out.  What is FractalForums.com doing right that Deviant Art, Renderosity, the Ultra Fractal Mailing List and so many other community venues  (largely dead and forgotten) have been failing at?  Half the postings there on FractalForums.com annoy me and the other half seem unimportant.  Is that the magic combination for a vibrant and self-sustaining community site?  Something for everyone and a steady stream of provocation?

The web-rings are no longer breathing.  They were a great idea in the 90’s but Google has done a better job of locating fractal art sites for the last 10 years.  The community art sites are brain-dead; Flickr’s beginners out-perform Deviant Art’s masters on a regular basis these days.  I have no idea why FractlForums.com should be thriving in such a wasteland, but it is.  Maybe there’s something about the social environment at FractalForums.com that draws in people from the old stuffy places? –and keeps them coming back.  Something nourishing and enticing?  What could it be?

Even I’ve joined in on some of the threads over there and I almost always avoid opening my mouth in a forum these days.  If a place like that can engage someone as jaded as me then there must be something special going on, whatever that invisible quality might be.  I’m even reviewing their contest and I find art contests distasteful.   Based on all that, I guess I ought to say that the first prize should go to FractalForums.com themselves in the category of Most Relevant Fractal Art Community Site.

The email tells me that there’s three categories to the contest and that they’ve been carefully defined.  But the first lesson in judging art is to stop listening to the people around you and ignore the boundaries they’ve constructed.  Trust no one.

I’ve made up my own categories and the first is a general one and I call it the At Last! Something I Wish I’d Made And Could Take Credit For –category.

And the winner is…

My Secret Garden by SaMMy. Click to view full-size at FractalForums.com.

My next category is one which most fractal artists will immediately relate to.  I call it the Astonishing Thing That I Cannot Describe –category.  The winner is obvious, but only if you view the image full-size.  For that reason I’ve only included a link.  No thumbnail or fair-use version can do justice to this great golden vision.  You have to go there and see it life sized or not at all.

Next, a category for which there was really only one serious contender.  The Best Rendition of Bocklin’s Isle of the Dead I’ve Seen Recently –category.  The author calls it “Mandel-blob” but remember: when judging art stop listening to others even when it’s the artist themself speaking.  I think this one’s my favorite.  But that’s not a category.

Mandel-blob by Buddhi

Hey!  It certainly is the year of the Mandelbulb, isn’t it?  My next category is the Best Rendering of the Mandelbulb Formula, Now Let’s Move On To Something Else –category.   This one really is very nice.  I’m not being sarcastic; the coloring and shadows and detailing is very well done.  Congratulations, Kraftwerk, for making something new out of something that’s become rather stale very quickly.  Nice screen name too.  That isn’t a category but might be one worth adding next time.

Living Ornaments by Kraftwerk

Did I saw let’s move on from the Mandelbulb?  Next category is Second Best Rendering of the Mandelbulb Formula, This Could be a New Genre and the winner is Kraftwerk, again.  Maybe it all depends on how you render these formulas and not the formula itself.  There’s something majestic about this image.  It’s got something impressive and attention grabbing about it.  Back in the old days of vinyl records this would have made a great album cover.

Golden and Delicious by Kraftwerk

Next up is the Hey, I Like Those Colors But I Bet No One Else Will –category.  I don’t know why palettes like this are so uncommon.  There’s a real retro Sci-Fi mood to anything using these sorts of muted colors.  Maybe it just doesn’t appeal to the young folks? (I’m 45).

Thistledown by Dave Makin

The final category, the You’re A Better Man Than Me Gunga Din –category.  It’s an animation.  Two weeks of rendering?  For me, two minutes to render something is too long.  The winner is Buddhi with Flight Through BulbBox a very detailed and extensive 3d fractal tour.  Two weeks!  He must have more than one computer.

Wait, one more category:  Not Really Part of the Contest But It Should Have Been.  I guess these stills in the animation section were just meant to be placeholders or something, but this one looks great.

Dangerous Spaceship by "bib" (not bub!). Click to go to FractalForums.com page for video.

I’d say Dangerous Spaceship is one of the top five images.  And I’ll bet it’s not even part of the contest, technically speaking.

Well, contests are like that.  The winners don’t always win.