Image:Verhulst-Mandelbrot-Bifurcation.jpg

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Image:Verhulst-Mandelbrot-Bifurcation.jpg

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Description

English: Diagram showing the connexion between Verhulst dynamic and Mandelbrot set

Source

self-made

Date

2008-04-07

Author

Georg-Johann Lay

Permission
( Reusing this image)

I, the copyright holder of this work, hereby release it into the public domain. This applies worldwide.

In case this is not legally possible:
I grant anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law.

Note

The Verhulst process

$v_k : x\mapsto kx(1-x)$

is equivalent to the process

$f_c: z\mapsto z^2+c$

by means of a linear transformation $Φ$ , i.e.

$\Phi^{-1} \circ v_k \circ \Phi = f_c$

Just let

$\Phi: x \mapsto \tfrac{1}{2}-\tfrac{1}{k}x$

and observe that the Parameters $c$ and $k$ are connected via

$1-4c \,=\, (k-1)^2$

File history

Click on a date/time to view the file as it appeared at that time.

	Date/Time	Dimensions	User	Comment
current	12:11, 14 April 2008	1,000×1,247 (157 KB)	Georg-Johann	(better quality)
	16:35, 7 April 2008	1,400×1,920 (271 KB)	Georg-Johann	({{Information \|Description= \|Source=self-made \|Date=2008-04-07 \|Author= Georg-Johann Lay \|Permission={{PD-self}} \|other_versions=- }} )

File links

The following pages on Schools Wikipedia link to this image (list may be incomplete):

Mandelbrot set

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