Random IFS

Same Picture

First, fix a resolution, usually one pixel, to which the picture is to be rendered.

We show

long enough addresses specify regions smaller than a pixel,

that randomness guarantees all finite addresses are visited by the points generated by the random IFS algorithm, and

that consequently every pixel of the attractor is visited.

Diameter goes to 0 under iteration of any contraction map. The basic idea in showing how the Random IFS algorithm fills to given resolution the attractor of the Deterministic IFS algorithm. Iteration and address shift: how iteration affects the address of the points generated by the Random IFS algorithm. The role of randomness in filling up the attractor: why applying the transformations in a repeating pattern won't fill up the attractor. Example illustrating the fill. Some other issues about the Random IFS algorithm

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