These images are based on the famous Mandelbrot Set equation.
They are from a series called Genetic Compositions.
They are like abstract paintings or sculptures, except they
are not designed physically, or manually. They are compositions,
but were not composed in a spatial domain, rather, they were
composed in a genetic space. The resulting organic, gestural
forms are born of a technique more akin to genetic engineering
than to painting. Each image in this set was created by carefully
tweaking the real and imaginary components of the Mandelbrot
equation, and viewing the results, many times, until satisfactory.
In my head, a slow, subconscious genetic algorithm is unfolding as I re-tweak, re-evaluate, refine these images. Genetic algorithms are the computational equivalent of Darwinian evolution, which is a creative process that happens over millions of years. Here is a page about a technique which uses a genetic algorithm to tweak Mandelbrot images:
developed as part of
a collaborative installation coordinated
by artist and curator Stephanie (Portico) Bowman, exhibited at the
Koehnline Museum of Art, in Chicago, September 2005.
Below are other versions you can download:
(bowman.exe) (Bowman_reg.exe) (Bowman_big.exe) (Bowman_red.exe) (Bowman_big_big.exe) (Bowman_big_big_slow.exe) (Bowman_big_big_fast.exe)
Genetic Space (photo-series)
This image represents the nine tweaks that were used to create a photo-series called Genetic Space. The middle image is the Mandelbrot Set untweaked. Images to the left, right, top, and bottom show the result of tweaking certain selected genes. The artwork, approximately 4ft. X 4ft., consists of 9 black&white exposures printed on color paper, with a slight sepia tint.
Some mathematicians, as well as artists, artistically-inclined mathematicians, and mathematically-inclined artists, really love iterating in the complex plane. It's an activity analogous to the repeated expression of a genetic code, which happens with each cell division. With every iteration, more complexity emerges. Organic forms such as the Mandelbrot set are generated with this process. These forms are examples of fractals, and each fractal is a portrait of one unique function. Every individual fractal is one creature in a vast range of possible creatures. There are parts of their functions which can vary, and so they can be mutated and re-expressed to generate creatures with varying anatomies. All fractals are members of a complex and infinite family tree. A taxonomy of fractal families is being systematically uncovered, by geometers and chaos-lovers, like Clifford Pickover and Michael Barnsley.
(a 5 by 5 image of a different Genetic Space)
Richard Dawkins, in The Blind Watchmaker, describes the evolution of a species in terms of a range of possible genetic states. Necessity for that species to adapt to its environment limits the possibilities of its genetic states. If all the genes of that creature are considered as axes in a large multidimensional space, then its evolution can be seen as a trajectory in that space. The trajectory represents genetic mutations, and its general trend is towards better adaptability with its changing environment. This is what Dawkins calls "animal space."
These nine images are mutations of the Mandelbrot set. They show two axes of mathematical mutation - one vertical and one horizontal. The middle image shows the Mandelbrot set with no mutations. The genes which are mutated are not explicitly identifiable. They were selected, not for mathematical rigor, but for their adaptability to the artist's aesthetic model.
Here's something I wrote about a technique for taking the Mandelbrot set equation and tweaking components of it so as to generate many interesting forms. It uses biological analogies. Interaction with the software allowed for rapid visual feedback to making small changes, such that one could quickly change parameters and see the results rapidly. This enabled me to tweak my way throught the huge genetic space of aesthetic possibilities, at a pace approximating sculpture or painting. Here it is.
What happens when you take an X ray of the Mandelbrot Set? Well, what on Earth is that supposed to mean? This is what I call images of the Mandelbrot Set that show something more than merely the resulting value of iterating the equation a number of times. Mandelbrot X-rays show something of the character of the equation as it iterates. Check it out.