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

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 have certainly moved me on to the next island.  Actually, I don’t care if a voyage like this never ends.

3 thoughts on “Fractals Don’t Have to be Fractals

  1. Thanks for the article :) There are people out there who seem to take the fractal medium very seriously :) If you have the patience to dive in the sea of pretty pictures there’s a few pearls that will inspire (much like my experience of the rest of the art world :D )

    I feel a bit limited in continually jumping on the boat of discovery.. hunting around for something exciting, whilst interesting to me in its own right, is not really the process I want to go through. The skill in being able to intentionally compose an image is really what I’m looking for. I’d imagine a big part of that is down to experience with the formulae and understanding the maths behind it, but considering the vast difference in image you can get through tiny modifications in parameters, and considering its chaos I’m playing with, am I reaching towards a star I’ll never touch? I’m not sure hehe. Any thoughts? :)

  2. Thanks for your comments. “surpass most of nature” –yes, I think that’s quite true. In fact, I think fractals have their own “nature” and create a new kind of natural imagery. Although there’s a lot of variety in say, rain forest plants and animals, fractals seem to have an almost unlimited creativity of which the latest 3D variety of Mandelbulbs and Mandelboxes are just a beginning. It’s an exciting time in the fractal world right now.

  3. Nice piece. I would perhaps reverse the notion about fractals attempting to be like ‘art’, and instead say that some of the best art (and indeed nature) attempts to contain fractal-like qualities. Some of the pictures in this post, (and others like “Before the rain”) actually surpass most of nature in my opinion. Trees and greenery in the real world often tend to look fairly drab and boring, and fractal material like the aforementioned would be preferred.

    Like you, I look forward to viewing (and rendering myself) more awesome Mandelbox creations. I suppose it could be considered less ‘organic’ than the Mandelbulb, but has more variety and it’s still capable of very organic stuff anyway (What does Terry think of the Mandelbox?). I still think though that the real 3D Mandelbrot (when and if it’s found) will combine some of the best qualities of both the Mandelbox and bulb, and yes, be even more fantastic.

    My hunt for it has taken a back seat these past few months to work on my raytracer and ‘RealLife’ ™ – soon time to get back on the trail I reckon :)

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