MandelbrotSetPlot
MandelbrotSetPlot[{zmin,zmax}]
plots the portion of the Mandelbrot set inside the rectangle with corners zmin and zmax.
plots the Mandelbrot set over a default rectangle.
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 
. - The default rectangle for MandelbrotSetPlot[] has corners
and 
. - MandelbrotSetPlot produces a Graphics object containing a Raster primitive.
- MandelbrotSetPlot[] has the same options as Graphics, with the following additions:
-
ColorFunction Automatic how to determine the color of a pixel EscapeRadius 2 how to determine that a point is not in the set Frame True whether to draw a frame around the plot ImageResolution 500 resolution of the image in the larger direction MaxIterations 1000 maximum number of iterates per point PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends for the number of interactions PlotTheme $PlotTheme overall theme for the plot - With MaxIterations->n, where n is a positive integer, the function
will be iterated at most n times to determine if the orbit of 0 ever exceeds 2. - With ColorFunction->f, where f is a function, the argument of f is a real number in
proportional to the number of iterates, and f must return color directives, such as RGBColor and Hue, or named colors, such as Red and Blue. - ColorFunction->"name" is equivalent to ColorFunction->(If[#1,Black,ColorData["name"][#]]&).
- The list of possible color function names is given by ColorData["Gradients"].
Examples
open allclose allBasic Examples (3)
Options (9)
ColorFunction (5)
ImageResolution (1)
Increase ImageResolution for finer plots:
MaxIterations (1)
Increase MaxIterations to improve quality when zooming in:
Properties & Relations (3)
Points in the Mandelbrot set determine quadratic Julia sets:
Use MandelbrotSetMemberQ to determine whether a point is in the Mandelbrot set:
MandelbrotSetIterationCount gives the number of iterations used to determine if a point is not in the Mandelbrot set:
Text
Wolfram Research (2014), MandelbrotSetPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/MandelbrotSetPlot.html.
CMS
Wolfram Language. 2014. "MandelbrotSetPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/MandelbrotSetPlot.html.
APA
Wolfram Language. (2014). MandelbrotSetPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/MandelbrotSetPlot.html