# Wolfram Language & System 10.4 (2016)|Legacy Documentation

This is documentation for an earlier version of the Wolfram Language.
BUILT-IN WOLFRAM LANGUAGE SYMBOL

# MandelbrotSetPlot

MandelbrotSetPlot[{zmin,zmax}]
plots the portion of the Mandelbrot set inside the rectangle with corners and .

plots the Mandelbrot set over a default rectangle.

## Details and OptionsDetails 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 has corners and .
• MandelbrotSetPlot produces a Graphics object containing a Raster primitive.
• 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 , 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 , 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"].

## ExamplesExamplesopen allclose all

### Basic Examples  (3)Basic Examples  (3)

Show the whole Mandelbrot set:

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Zoom in and change the color:

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Show a legend of the number of iterations:

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