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2009-08-31 Fractals in traditional art

2009-08-23 Gigapixel panorama

2009-08-21 Yellowstone's abstract art

2009-08-20 Pollock & fractals? A hoax.

2009-08-04 Kunstformen der Natur

2009-08-02 The Fibonacci fractal

2009-07-29 The art of Kris Kuksi

2009-07-22 Group exhibition

2009-06-20 Kusama's patterns II

2009-06-14 Kusama's patterns

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August 31st 2009

Fractals in traditional art

The "Pollock and fractal hoax" made me think about the conditions a traditional (or algorithmic...) artwork should satisfy to be reasonably called fractal. Taylor & co. tried to use a mathematical tool (namely the box counting procedure) to assess the fractal quality of Pollock's artwork, but this attempt failed, given that even childish drawings (see the blog post) showed the same signature, while it would occur to nobody to call them fractal. Maybe we should be a bit more modest and start with a set of informal conditions.

By defintion, mathematical fractals display structures on an infinite scale range. For obvious reasons, we cannot apply this definition literally to physical obects, such as paintings. We can replace "infinite" by "wide", ie. call a physical object fractal if it displays structures on a scale range comprising a reasonable number of orders of magnitude. There is of course no rational way to decide what is a "reasonable number of orders of magnitude". The tendency seems to accept that two or three orders of magnitude are sufficient. Such a definition does not make sense in my opinion. Except for very specific man-made artifacts, any physical object you could think of does display structures on two or three orders of magnitude. The laptop I'm writing on now is around 40cm large, and does have features no larger than 0.5mm. That's three orders of magnitude. If we are considering paintings, then any painting roughly one meter large and featuring one milimeter details (what is quite common among figurative works) should be called fractal. As it stands, such a loose definition is simply meaningless. On the other hand, if we decide for, say, five orders of magnitude, then no reasonably sized work of art could qualify.

In a previous blog post, I featured the sculptures of Kris Kuksi, and mentionned it as an interesting example of "non computer-generated art with fractal characteristics". In hindsight, there are three reasons that made me use the word "fractal".

  • The artist pushed the physical limits of the medium to display details as small as possible. You generally do not expect sculptures to have submilimetric features, Kuksi's sculptures do.
  • The details have as much artistic importance as the global structure of the work. On his deviantart page, Kuksi displays several photographs of each work, to exhibit details invisible on the global view.
  • Self-similarity is present, through characters and objects of various sizes.

I think these three pragmatic criterions give a starting point to determine the fractal character of a work. A mathematical criterion which could be tested objectively would be more desirable, but we have seen that it is maybe too much to hope for. According to these three criterions, I probably could call fractal some of Pollock's paintings, like Lavender Mist displayed below.
Lavender Mist, Pollock

Jackson Pollock, No.1 - Lavender Mist (1950), oil, enamel and aluminum on canvas, 221 x 299.7 cm. See the page of the National Gallery for more informations.

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