Genetic generalized iterative functions in the complex plane

Having realized that an arbitrarily large number of brand new fractal functions could be constructed by genetic algorithms residing in an image-generating system, I added a new type of genome to my existing system. The new "DNA" codes for a tree of functions accepting two complex number arguments and returning a single complex number.

In Primordial Soup mode, the genetics constructs arbitrary expressions of nested complex functions, along with numerous constants, attractor escape radii, conditions for exiting the inner iteration loop, the type of measure of distance to the attractor, etc.

I scout for initial seed individuals in Primordial Soup mode, then begin a genetic run with the starting seeds. Aesthetic fitness scores are assigned as usual, and soon "fractal sex" is happening, along with mutation in various proportions. Hence the genetics finally gets down inside the fractal iteration loop. Simple quadratic Mandelbrot or Julia Set functions can emerge if the complex operators "plus" and "multiply" are present. But the real value comes when the genetics generates weird tangled functions that don't look like anything you see in the fractal image literature.

The images on this page are all pure generalized iterative functions, i.e. I constrained the runs to root a single genlIter(x,y) function at the top, with maybe a few (genlIter(x,genlIter(x,y)) thrown in, but no other outer genetic functions. This page shows just the genetic fractals themselves, not hybridized with other genetic image strains.

Pressing on an image below will download a larger version, between about 20k and 60k.

one of first new genetic complex plane fractals, exp(c/z)

genes produced sin(tanh (sin(cosh (1/z) - c)))

same, zoomed

cos (cosh (div (tanh (sub (tanhO (c,z),z), div(tanhO(div (c,z), z), z))))

way too long to print; 44 nested complex functions, constants, coordinates

24 nested functions

sin (recip (cos (div (c,z))))

recip (div (sinh (c/z)), complex (1.73,-0.90)))

sin (recip (cos (c/z))))

sin (recip (cos (c/z)))


7-19-99 hyperfractal