These are fractals generated through an interative process. They are created by applying the same equation repeatedly to a complex number and observing the convergence of the iterative process.
Two types shown are denoted as Mandelbrot type and Newton type fractals.
In both cases an arbitrary color palette is chosen, a set of N colors, so that after the nth iteration the point is sufficiently large and is diverging then we assign the n mod N color to that point.
You are probably familiar with graphing functions(y=mx+b). The plane which we graph on essentially pairs every possibility of the input domain with the output domain(range). However, with complex numbers this poses a challenge since a similar method would require 4 spacial dimensions to view the graph. To reconcile this we use colors(RGB or CMYK) to represent the important aspects of the graph.
Red(Cyan) represents the proximity of a zero of the function. E.g if f(z)=0 then z is colored red.
Green(Magenta) represents the distance from the original point. E.g |f(z)-z| determines green.
Blue(Yellow) represents the angle from the original point. |arg(z)-arg(f(z))|
Fractals and Complex Maps are available for purchase on metal(16x16 and 30x40), woven blankets (50x60 and 60x80), and prints (30x40).
Please reach out via email while I develop the store page.
