MandelbrotSetMemberQ

MandelbrotSetMemberQ[z]
returns True if z is in the Mandelbrot set, and False otherwise.

Details and OptionsDetails and Options

  • The Mandelbrot set is the set of all complex numbers 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 if the sequence diverges.
  • The default setting is MaxIterations->1000.
  • If the maximum number of iterations is reached, z is assumed to be in the Mandelbrot set.

ExamplesExamplesopen allclose all

Basic Examples  (3)Basic Examples  (3)

Test whether is a member of the Mandelbrot set:

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Zero is known to be inside the Mandelbrot set:

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It takes a few hundred iterations to determine that 0.2501 is not in the Mandelbrot set:

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Introduced in 2014
(10.0)