Fractals - IFS

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An iterated function system is a handful of affine maps. Each row of a system is seven numbers a b c d e f p: it takes a point (x, y) to (a x + b y + e, c x + d y + f) and is picked with probability p. Start anywhere, pick a map at random by the probabilities, apply it, plot the point, and repeat a million times: the points pile up on the attractor, the fractal the maps describe, whatever the starting point. The 3D page does the same with thirteen numbers a row.

The systems are in one text file, fractint.ifs, in Fractint's format. They are Fractint's own (the Sierpinski triangle, the fern, the coral and the others of its fractint.ifs), the five of Anthony Hanmer's from Fractint 20's fract205.ifs, and two of mine (xx and lars). I checked every system of Fractint's against the file: the numbers are identical. The next map is chosen as Fractint chooses it: the probabilities are added up in order until the sum reaches a random number between 0 and 1, so when they add up to less than 1 the last map takes what is left, and a negative probability (the first row of DC022b6c has one) is never chosen.