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Author Topic:  feigenbaum stretch  (Read 674 times)

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Offline claude

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feigenbaum stretch
« on: November 05, 2018, 09:51:59 PM »
feigenbaum stretch



https://fractalforums.org/index.php?action=gallery;sa=view;id=1653

Mandelbrot set with Feigenbaum point stretched off to -infinity at the left by exponential / logarithmic transformation

Linkback: https://fractalforums.org/index.php?topic=2112.0

Offline Adam Majewski

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Re: feigenbaum stretch
« Reply #1 on: November 05, 2018, 11:07:27 PM »
Cool
Can you add more components to the image ? (until image get dark)
Where is the code ?
Can you describe algorithm ( transformation) ?



Offline gerrit

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Re: feigenbaum stretch
« Reply #3 on: November 06, 2018, 04:26:29 AM »
Transform is \( c \leftarrow e^c + c_0 \) with \( c_0 = −1.401155189092051. \)
How do you find \( c_0 \), or other Feigenbaum points?
It's a fun map. Here's one for the Fbm point defined by going to period 3 mini, then it's relative period 3 mini, etc.

Offline claude

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Re: feigenbaum stretch
« Reply #4 on: November 06, 2018, 05:39:58 AM »
How do you find \( c_0 \), or other Feigenbaum points?

https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/bin/m-feigenbaum.c estimate location of period 2P atom using size of period P island, use Newton's method to find its nucleus and size more precisely, repeat
https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/bin/m-feigenbaum3.c estimate location of tip of antenna (renormalized from -2+0i) of period P island using size estimate, from there find nucleus of period 3P island using Newton's method, repeat

Offline gerrit

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Re: feigenbaum stretch
« Reply #5 on: November 07, 2018, 04:30:10 AM »
https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/bin/m-feigenbaum.c estimate location of period 2P atom using size of period P island, use Newton's method to find its nucleus and size more precisely, repeat
https://code.mathr.co.uk/mandelbrot-numerics/blob/HEAD:/c/bin/m-feigenbaum3.c estimate location of tip of antenna (renormalized from -2+0i) of period P island using size estimate, from there find nucleus of period 3P island using Newton's method, repeat
Neat, and it also shows why there are uncountably many Feigenbaum points.

Offline Adam Majewski

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Re: feigenbaum stretch
« Reply #6 on: October 17, 2019, 07:12:19 PM »


clip
Mandelbrot Feigenbaum

Started by trafassel on Fractal Mathematics And New Theories

1 Replies
374 Views
Last post December 14, 2019, 09:47:48 PM
by trafassel
clip
m-streching-feigenbaum from mandelbrot-graphics library by Claude

Started by Adam Majewski on Programming

3 Replies
354 Views
Last post October 17, 2019, 07:13:50 PM
by Adam Majewski