MandelbrotSetPlot

MandelbrotSetPlot[{zmin,zmax}]

plots the portion of the Mandelbrot set inside the rectangle with corners zmin and zmax.

MandelbrotSetPlot[]

plots the Mandelbrot set over a default rectangle.

Details and Options

Examples

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Basic Examples  (3)

Show the whole Mandelbrot set:

Zoom in and change the color:

Show a legend of the number of iterations:

Options  (9)

ColorFunction  (5)

Use a built-in color function to color by a scaled number of iterates:

Modify a built-in color function:

Use a named color gradient:

Zoom in to see more detail and colors:

Write a custom color function:

Color all points that escape in less than 10 iterations:

EscapeRadius  (1)

Increasing the escape radius can smooth the transitions between colors:

ImageResolution  (1)

Increase ImageResolution for finer plots:

MaxIterations  (1)

Increase MaxIterations to improve quality when zooming in:

PlotTheme  (1)

Use a theme with simple ticks and a bright color scheme:

Change the color scheme:

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:

Neat Examples  (1)

Turn the complement of the Mandelbrot set into a checkerboard:

Introduced in 2014
 (10.0)