plots the Julia set of the rational function f of the variable z.
plots the Julia set of the function .
Details and Options
- The Julia set of a function f is the closure of the set of all repelling fixed points of f.
- JuliaSetPlot has the same options as Graphics, with the following additions and changes:
AspectRatio Automatic ratio of height to width of the plot Axes False whether to include axes ColorFunction Automatic how to color the exterior ColorFunctionScaling True whether to scale arguments to ColorFunction Frame True whether to include a frame ImageResolution Automatic resolution of points in the Julia set MaxIterations Automatic how many iterations to allow for each point Method Automatic the method to generate the image PerformanceGoal $PerformanceGoal aspects of performance to try to optimize PlotLegends None legends for the number of interations PlotRange Automatic range of values to include PlotRangeClipping True whether to clip at the plot range PlotStyle Automatic graphics directives to specify the style for each point PlotTheme $PlotTheme theme to use for styles and appearances
- The possible methods are "InverseIteration", "EscapeTime", and "OrbitDetection".
- With Method->"InverseIteration", JuliaSetPlot produces a ListPlot showing individual points of the Julia set.
- With Method->"EscapeTime" or with Method->"OrbitDetection", JuliaSetPlot produces a Graphics object containing a Raster primitive.
- 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"].
Examplesopen allclose all
Basic Examples (4)
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:
Show the points in the Julia set:
Use a theme with simple ticks in a high-contrast color scheme:
Increase ImageResolution for finer plots:
By default, the points are not shown unless ColorFunction->None:
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" method option is too low for a rational function, no points may be returned:
Wolfram Research (2014), JuliaSetPlot, Wolfram Language function, https://reference.wolfram.com/language/ref/JuliaSetPlot.html.
Wolfram Language. 2014. "JuliaSetPlot." Wolfram Language & System Documentation Center. Wolfram Research. https://reference.wolfram.com/language/ref/JuliaSetPlot.html.
Wolfram Language. (2014). JuliaSetPlot. Wolfram Language & System Documentation Center. Retrieved from https://reference.wolfram.com/language/ref/JuliaSetPlot.html