Details 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.
Examplesopen allclose all
Basic Examples (3)
Test whether is a member of the Mandelbrot set:
Zero is known to be inside the Mandelbrot set:
It takes a few hundred iterations to determine that 0.2501 is not in the Mandelbrot set:
Sometimes MaxIterations needs to be increased to eliminate false positives:
Generate the Mandelbrot set from randomly chosen points:
Approximate the first point along the line that is not in the Mandelbrot set:
Show the point on the Mandelbrot set:
Neat Examples (4)
MandelbrotSetMemberQ can be used to get an estimate of the area of the Mandelbrot set:
Display the Julia sets for points in the Mandelbrot set:
Rotate the Mandelbrot set:
Use MandelbrotSetMemberQ to distinguish Julia sets that are Cantor sets:
Introduced in 2014