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 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 (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} , (with$z_{0}$=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