JuliaSetPlot

JuliaSetPlot[f,z]

plots the Julia set of the rational function f of the variable z.

JuliaSetPlot[c]

plots the Julia set of the function .

Details and Options

Examples

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Basic Examples  (4)

Generate the filled Julia set of :

Generate the Julia set:

Show the filled Julia set with the points in the Julia set:

Show a legend of the number of iterations:

Scope  (7)

JuliaSetPlot[c] generates the Julia set of a function of the form :

Generate the Julia set of a polynomial:

Generate the filled Julia set of a rational function:

Change the color function:

Show the points in the Julia set:

Show just the points:

Use a theme with simple ticks in a high-contrast color scheme:

Options  (19)

AspectRatio  (2)

The default aspect ratio uses equal scales for and :

Specify a different ratio:

Background  (1)

Use a black background as contrast with the points in the Julia set:

ColorFunction  (3)

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

Zoom in to a region to see more details:

Use a named color gradient:

Write a custom color function:

Frame  (1)

Turn Frame off:

FrameLabel  (1)

Use FrameLabel to label the complex plane:

FrameStyle  (1)

Use FrameStyle to change color:

FrameTicks  (1)

Turn frame ticks off:

ImageResolution  (1)

Increase ImageResolution for finer plots:

PerformanceGoal  (2)

Generate a higher-quality plot:

Emphasize performance, possibly at the cost of quality:

PlotLegends  (1)

Legends show the number of iterations:

PlotRange  (2)

The plot range is chosen automatically, based on the Julia set:

Zoom in to a region to see more details:

PlotStyle  (2)

By default, the points are not shown unless ColorFunction->None:

Specify the plot style:

PlotTheme  (1)

Use a theme with increased contrast and axes:

Possible Issues  (4)

JuliaSetPlot only works with rational functions:

When using orbit detection, sometimes no attractive orbits are detected:

If the value of the "Bound" option is too low for a rational function, no points may be returned:

Some very large Julia sets can take a long time to compute:

Neat Examples  (1)

Colorize the components of a Julia set:

Introduced in 2014
 (10.0)