8.3: Distance Estimator algorithms
- Page ID
- 102626
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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.