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  to the ratio
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.
The applet use the Boundary Tracing algorithm too. Therefore these spots disappear under enlargement.
 John W. Milnor "Dynamics in One Complex Variable" Appendix G. Remarks on Computer Graphics.