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.

The distance estimate for Julia sets is very close [1] to the ratio
|G|/|G'|, where
G(z .
_{o}) = lim
_{k®¥}
log|z_{k}|/n^{k}
|G'(z _{o})| = lim
_{k®¥}
|dz_{k}/dz_{o}| / (n^{k}|z_{k}|)For quadratic maps ( n = 2)
dz .
_{k}/dz_{o} = 2^{k}z_{k-1}
... z_{o}When one of z is small (e.g. in the center of the
picture at _{i}z) the distance estimate diverges therefore
we get the central spot and its preimages.
_{o} = 0The applet use 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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