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mandelbrot 1 mandelbrot 3

basis: mandelbrot-fractal

z(0) = c = pixel;
z(n+1) = z(n)² + c.

Two parameters: real and imaginary perturbations of z(0)

mandelbrot 2 mandelbrot 4 This set is the classic, named after Benoît Mandelbrot: the only one implemented in many plotting programs, and the source of most of the printed fractal images published in recent years. It is simply a graph: the x (horizontal) and y (vertical) coordinate axes represent ranges of two independent quantities, with various colors used to symbolize levels of a third quantity which depends on the first two. So far, so good: basic analytic geometry.