Difference between revisions of "Manuals/calci/MANDELBROT"

Revision as of 16:49, 22 August 2017

MANDELBROT

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 $z_{n+1}={z_{n}}^{2}+c$ , (with $z_{0}$ =0), where points c in the complex plane for which the computed value of $z_{n}$ does not tend to infinity.

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 *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 <math>(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,...)</math>  where the result does not approach infinity.
+*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 <math>(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,...)</math>  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 <math>z_{n+1}={z_n}^2+c</math>, (with<math>z_0</math>=0), where points c in the complex plane for which the computed value of <math>z_n</math> does not tend to infinity.