This is a list of techniques that could be useful as part of a generative art toolbox; in alphabetical order:
Abbreviated as EA.
Sometimes called morphogenetic algorithms.
Paul Harrison at eu-gene wrote:
Levy flights are pretty cool. I agree with the second url that this has nothing to do with free will, but Levy flights are a nice way to add at least the _illusion_ of free will. Here’s an example comparing a Levy flight (left) with a simple Gaussian random walk (right):
Something every generative artist should have in their toolbox, in my opinion. Cauchy distribution is particularly easy to generate, it’s just norrmally-distributed-random-value divided by normally-distributed-random-value. Random samples from other members of the Levy-stable family can be generated, but the formula is a bit more involved.
“The Gray-Scott reaction diffusion model is a member of a whole variety of RD systems, popular largely due to its ability to produce a very varied number of biological looking (and behaving) patterns, both static and constantly changing. Some patterns are reminiscent of cell devision, gastrulation or the formation of spots & stripes on furry animals. As with all RD models, these patterns are the result of an iterative process evaluating each cell of the simulation space based on the concentrations of the two main parameters (for Gray-Scott usually named f and K) of the reaction equation as well as taking into account the concentrations of these 2 substances in neighboring cells. So conceptually the reaction diffusion system lies somewhere between the isolated DLA process working with individual particles and the entirely rulebased evaluation of a cell’s neighborhood in traditional cellular automatas, which we will deal with in the next post.”
One of the most general yet compelling mathematical principles that can be applied, especially to visuals. Popular thanks to M.C. Escher and the Droste tin can. Recursion is a fundamental feature of the logical programming paradigm as implemented by the Prolog language. From WikiPedia:Recursion:
“In order to understand recursion, one must first understand recursion.”
“If you already know what recursion is, just remember the answer. Otherwise, find someone who is standing closer to Douglas Hofstadter than you are; then ask him or her what recursion is.”