estimates the distance from c to the nearest point in the Mandelbrot set.
estimates the distance from c to the nearest point in the complement of the Mandelbrot set.
Details and Options
- The Mandelbrot set is the set of all complex numbers c for which the sequence does not diverge to infinity when starting with .
- With the option MaxIterations->n, the sequence will be iterated at most n times to determine the distance. The default setting is MaxIterations->100.
- As MaxIterations approaches infinity, MandelbrotSetDistance[c] will converge on a number that is guaranteed to be at least the true distance.
Examplesopen allclose all
Basic Examples (2)
MandelbrotSetDistance is useful for making stark binary images of the Mandelbrot set: