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


open allclose all

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:

Wolfram Research (2014), MandelbrotSetPlot, Wolfram Language function,


Wolfram Research (2014), MandelbrotSetPlot, Wolfram Language function,


Wolfram Language. 2014. "MandelbrotSetPlot." Wolfram Language & System Documentation Center. Wolfram Research.


Wolfram Language. (2014). MandelbrotSetPlot. Wolfram Language & System Documentation Center. Retrieved from


@misc{reference.wolfram_2024_mandelbrotsetplot, author="Wolfram Research", title="{MandelbrotSetPlot}", year="2014", howpublished="\url{}", note=[Accessed: 22-July-2024 ]}


@online{reference.wolfram_2024_mandelbrotsetplot, organization={Wolfram Research}, title={MandelbrotSetPlot}, year={2014}, url={}, note=[Accessed: 22-July-2024 ]}