MandelbrotSetDistance

MandelbrotSetDistance[c]

estimates the distance from c to the nearest point in the Mandelbrot set.

MandelbrotSetDistance[c,"Interior"]

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.

Examples

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Basic Examples  (2)

Estimate the distance from to the Mandelbrot set:

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MandelbrotSetDistance is useful for making stark binary images of the Mandelbrot set:

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Scope  (2)

Options  (2)

Properties & Relations  (1)

Neat Examples  (4)

See Also

MandelbrotSetPlot  MandelbrotSetMemberQ  MandelbrotSetBoettcher  MandelbrotSetIterationCount

Introduced in 2014
(10.0)