Pauldelbrot’s Mandelbrot Safari and other Journeys into the Unknown

Back, several postings ago, when I reviewed the latest calendar, I heaped abuse on Pauldelbrot’s image from his Mandelbrot Safari series calling it retro and not cutting-edge.  The owner of and publisher of the calendar, Christian Kleinhuis, informed me that what Pauldelbrot was doing was in fact very cutting-edge as it was utilizing new methods that enabled him to zoom to a much greater extent than had previously been possible.  And something about a new coloring method too.

But as an illustration of how weird fractal art as an art form can be, Pauldelbrot’s work can be kicked and abused in one review and then praised in another, just a month later as you will soon see.

Let me explain this apparently senseless thinking:  For the calendar, I didn’t think Pauldelbrot’s work had commercial appeal (as well as just about everyone else’s work in the calendar); But in this posting I present his Mandelbrot Safari images as epitomizing the pastime of fractal exploration (and a fresh example of that) as well as a good example of classic-style fractal art.

But most importantly, I rather like many of these images myself for their own sake, and the fact that they’re from the Outer Limits just enhances that.  One shouldn’t talk too much about fractal art.  Perhaps most readers have already skipped to the pictures.

The best way to follow the Mandelbrot Safari is by reading its own forum thread on  More images, comments, etc…  Who knows?  You might even decide to buy one of the FFs 2012 calendars for no other reason than because it contains one of these Safari images.  Now wouldn’t that make me look stupid after saying they had no commercial appeal?  Buy a calendar —fight the man!

~Click on images to go to original forum thread with larger images in it~

The initial image from Pauldelbrot’s Mandelbrot Safari thread

The safari begins:  fairly common terrain we’re starting off from on May 4th, 2012.  Doesn’t look particularly promising, I must say.  But I’m not the pilot or the navigator on this expedition.  Let’s wait and see what’s over the horizon.  I’m sure he’s got some exotic destination in mind.

evdz1_008_lrg by Pauldelbrot

The game is afoot, as Sherlock Holmes would say.  That’s an odd looking color to be seeing out in this sargasso sea of yellow.  The perennial question:  Where does it go?

evdz1_017 by Pauldelbrot

I jumped ahead a few of Pauldelbrot’s image postings and here we are at the first of many “portals” to the (glittering) unknown.  If you’re anything of a fractalnaut, you ought to be getting excited right now because it looks like this trip is 1. never going to end, and 2. going to be full of surprises.

evdz1_018_lrg by Pauldelbrot

A comment:

Is that the coloring of Pauldelbrot’s image, or of this guy’s hefty signature?  (sorry, couldn’t resist; it’s the duty of everyone on the internet to stamp out signature lines and other forms of “junk mail” content)

evdz1_029_lrg by Pauldelbrot

According to the thread, we’re now zoomed into about 4 e30 magnification.  That’s 4 and thirty zeroes behind it.

evdz1_044 by Pauldelbrot

Pauldelbrot answers a tech question in the thread here about what program he’s using:

…a mix of custom and off-the-shelf code here. Time on these has increased but the latest few have taken a few hours each. The iterations are still pretty low (around 5000) but the precision bits are getting fairly numerous.

A couple hours, each?  We’re obviously on the other side of some computing sound barrier.

evdz1_090 by Pauldelbrot

Note by author:

Now over 20,000 iterations in the shallowest parts of each image, and the magnification has just passed one googol, too…

Sound sci-fi -ish, doesn’t it?  What’s a googol?  Biggy big!  So big it’s covered with big-fur!  That’s the layman’s definition. (it’s this, actually: 10100)

Gets slower and slower with depth…

He’s doing this in Ultrafractal (UF) and makes this comment which sheds some light on the type of technical challenge all this is:

I should warn you that to get close to the quality results I’ve posted you’d need to use 3×3 AA, depth 2, nonadaptive AA because depth 1 isn’t enough oversampling and UF’s adaptive AA seems not to work as well as mine. The deeper images would thus need some very beefy hardware to render in anywhere near a reasonable time; or even a cluster rendering different tiles of the image per machine.

This is what Christian Kleinhuis, the owner (and sponsor) of must have meant when he told me Pauldelbrot’s image in the calendar was actually cutting edge imagery after all.

evdz1_113 by Pauldelbrot

The images are largely like this; circular and elegant, which is the sort of thing that characterizes classic fractal art –highly detailed, organized images.  I guess “complex geometric” is not a bad description, either.

Pauldelbrot says this in response to a comment about the great coloring:

It “discovers” colors, because it keeps shifting and blending them. Colors that are somewhat between pure primaries and secondaries, or somewhat desaturated as well as saturated, included, which may often be overlooked by humans doing things manually.

evdz1_204 by Pauldelbrot

“Overlooked by humans doing things manually”  Computers are more than just powerful paintbrushes.  It’s through this sort of exploration that one can develop a real appreciation for the machinery that they’re using.  That’s half the fun, I’d say.

I’ve just shown a sampling of images here; you’ll definitely want to check out the thread if you find these interesting.

evdz1_218 by Pauldelbrot

Some of the really dark images are the best in my opinion.  This one is from November 30th, 2012 and marks the 7th month of the safari.  It’s still going on, although, as Pauldelbrot said, the rendering gets slower because of the depth of the zoom.  Another image was posted just this week (Dec 11).

Pauldelbrot has embarked on a number of these zoom excursions with the same journey into the unknown feel to them.  Here’s some highlights from some of the others…

511_28_11_12_2_35_18 by Pauldelbrot

A note from this image, from a series entitled “Fall Woods 1”:

This zoom is near the Autumn Forest zoom. However, the area zoomed into is around a seahorse below and to the right of the green period-3 blob in Autumn Forest I. Out here, the “zero basin” doesn’t exist — there is no zero attractor at all. Where that happens, the basin implodes into a disconnected Julia set, which the surrounding seahorse shapes still try to conform to, with amazingly convoluted results!

Images in this series have mostly been rendered at 32000×24000 and downsampled for a whopping 625 samples per pixel, needed to render the “zero basin Julia” regions properly. I was able, nonetheless, to render most of them in under two hours.

Yeah, that’s 32 –thousand by 24-thousand.  Pauldelbrot is no wimp when it comes to making fractals!

511_03_11_12_12_37_51 by Pauldelbrot

511_02_11_12_12_20_32 by Pauldelbrot

Those above are two of my personal favorites from the Autumn Forest II and I series.  The disorienting vastness of fractal panoramas is easily seen in both as well as Pauldelbrot’s excellent coloring style.  In the process of trying to make fractals into art, I wonder how many of us forget how artistic fractals can be in their raw, freshly calculated form –if only we were to explore them and not the latest layering techniques more.

Lilac Exponent by Pauldelbrot, Sept 14, 2011

This is from more than a year ago.  It caught my eye back then because of the intense patterns of shapes and shapes and more shapes.  This sort of thing is an art form that only fractal algorithms can do and they do it very well, especially at the hands of someone as talented and creative as Pauldelbrot.

As Christian Kleinhuis was saying; Pauldelbrot has really done something new and different even if it does lie within the old category of “classic” fractal art.  I think Pauldelbrot has elevated that classical category higher with this kind of work and his probably represents the best of its kind.

Best of its kind so far, that is.  If Pauldelbrot’s herculean efforts and endless hours of rendering have shown one thing, it’s that there’s still much to be explored even in the realm of classical fractal imagery.  I hope he’s inspired a few others to follow this path, even if it takes them away from the seemingly much more advanced 3D fractals that most work on these days.

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