Manuals/calci/MANDELBROT

MANDELBROT (SettingsArray,Width,Height,MandeliterFunction,Shades,CanvasId)

Description

• This function shows the figure of the Mandelbrot.
• Fractals are infinitely complex patterns that are self-similar across different scales.
• This property is called self-similarity.
• Fractals form a never ending pattern, created by repeating a simple process over and over, in an ongoing feedback loop.Mandelbrot Set is the set of points in the complex plane with the sequence $(c,c^{2}+c,{(c^{2}+c)}^{2}+c,{{((c^{2}+c)}^{2}+c)}^{2}+c,{{{(((c^{2}+c)}^{2}+c)}^{2}+c)}^{2}+c,...)$ where the result does not approach infinity.
• The Julia Set is closely related to Mandelbrot Set.
• The Mandelbrot Set is obtained from the quadratic recurrence equation Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_{n+1}={z_n}^2+c} , (withFailed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_0} =0), where points c in the complex plane for which the computed value of Failed to parse (MathML with SVG or PNG fallback (recommended for modern browsers and accessibility tools): Invalid response ("Math extension cannot connect to Restbase.") from server "https://wikimedia.org/api/rest_v1/":): {\displaystyle z_n} does not tend to infinity.

Examples

1. MANDELBROT()

See Also

• FRACTAL
• LISSAJOUSCURVE
• LISSAJOUS

References

• Mandelbrot set

• List of Main Z Functions

• Z3 home