
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→∞} logz_{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_{k1} ... z_{o} . When one of z_{i} is small (e.g. in the center of the picture at z_{o} = 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.