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Circle Tiling    

Robert P. Munafo, 1996 Dec 19.

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A type of adjacency optimization, described in The Beauty of Fractals.

The basic technique is to use the distance estimator or interior distance estimator to define a circle, the entire interior of which is outside (or inside) the Mandelbrot Set. Then, any point on the edge of the circle can be fed into the distance estimator and new circles defined, continuing recursively to (theoretically) cover the entire area of interest.

In order to work well, an implementation of this algorithm must ignore circles smaller than a certain size and avoid areas that have already been covered by previous circles. Inaccuracies result from the fact that there are many areas that "ought" to be tiled by the algorithm but can't be reached because you have to go through a very narrow "channel" to get to them.

From the Mandelbrot Set Glossary and Encyclopedia, by Robert Munafo, (c) 1987-2024.

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