# Distance Estimator algorithm

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MaxIt = 3000

Distance Estimator algorithm is used in this applet. Color is "proportional" to log(dc), where dc is the approximate distance between the point c and the nearest point in the Mandelbrot set.

# "DE" algorithm and Julia sets

 The distance estimate for Julia sets is very close [1] to the ratio |G|/|G'|, where     G(zo) = limk→∞ log|zk|/nk     |G'(zo)| = lim k→∞ |dzk/dzo| / (nk|zk|) . For quadratic maps (n = 2)     dzk/dzo = 2kzk-1 ... zo . When one of zi is small (e.g. in the center of the picture at zo = 0) the distance estimate diverges therefore we get the central spot and its preimages. This script uses the Boundary Tracing algorithm too. Therefore these spots disappear under enlargement.

[1] John W. Milnor "Dynamics in One Complex Variable" Appendix G. Remarks on Computer Graphics.

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updated 12 Sep 2013