JuliaSetIterationCount

JuliaSetIterationCount[f,z,p]

returns the number of iterations, beginning with the complex number , of the function needed to determine whether p is in the Julia set of f.

JuliaSetIterationCount[c,p]

returns the number of iterations, beginning with the complex number , of the function needed to determine whether p is in the Julia set of .

JuliaSetIterationCount[f,z,{p1,p2,}]

returns a list of the number of iterations required to determine whether each member of {p1,p2,} is in the Julia set of f.

JuliaSetIterationCount[c,{p1,p2,}]

returns a list of the number of iterations required to determine whether each member of {p1,p2,} is in the Julia set of .

Details and Options

  • The Julia set of a function f is the closure of the set of all repelling fixed points of f.
  • JuliaSetIterationCount uses the same "OrbitDetection" algorithm as JuliaSetPlot.
  • With MaxIterations->n, where n is a positive integer, the function will be iterated at most n times to determine if z lies outside of the Julia set. If z is not found to lie outside the Julia set, JuliaSetIterationCount returns n+1. The default setting is MaxIterations->1000.
  • With WorkingPrecision->n, each iteration is internally calculated to n digits of precision. Without this option, the amount of precision used is determined based on the precision of p and the value of MaxIterations.

Examples

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Basic Examples  (2)

Four iterations are needed to determine that is not in the Julia set of :

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Out[1]=

Calculate the iterations for a list of numbers:

In[1]:=
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Out[1]=

Scope  (6)

Options  (2)

Properties & Relations  (3)

Possible Issues  (1)

Neat Examples  (2)

See Also

JuliaSetPlot  MandelbrotSetIterationCount

Introduced in 2014
(10.0)