returns the number of iterations of the function , beginning with , that are needed to determine whether c is in 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 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.
- For some points that the algorithm knows in advance to be inside the Mandelbrot set, MandelbrotSetIterationCount will return one greater than the value of MaxIterations.
Examplesopen allclose all
Basic Examples (4)
MandelbrotSetIterationCount works on all kinds of numbers:
Properties & Relations (1)
Possible Issues (1)
Neat Examples (3)
Make a Histogram of iteration counts along the imaginary axis:
Wolfram Research (2014), MandelbrotSetIterationCount, Wolfram Language function, https://reference.wolfram.com/language/ref/MandelbrotSetIterationCount.html.
Wolfram Language. 2014. "MandelbrotSetIterationCount." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MandelbrotSetIterationCount.html.
Wolfram Language. (2014). MandelbrotSetIterationCount. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MandelbrotSetIterationCount.html