Lyapunov fractals

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Offline ThunderboltPagoda

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« on: August 27, 2018, 02:31:38 AM »
Well, here are my first Lyapunov fractals. All images posted by me here are released to the public domain (Creative Commons CC0 1.0 Universal Public Domain Dedication), so you can do with them what you want.

Linkback: https://fractalforums.org/image-threads/25/lyapunov-fractals/1779/

Offline ThunderboltPagoda

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« Reply #1 on: August 27, 2018, 02:39:01 AM »
Another two, then it's enough for today.

Offline ThunderboltPagoda

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« Reply #2 on: August 27, 2018, 09:33:38 PM »
The unsuspecting anglerfish and the deep sea monster, the one-eyed frog and the crocodile in the desert. What does the crocodile in the desert? I have no idea.

Offline gerson

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« Reply #3 on: August 28, 2018, 05:21:26 PM »
Liked all.
See where the other frog's eyes stays...
https://www.deviantart.com/gs13/art/gs-deviant03-69035133

Offline ThunderboltPagoda

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« Reply #4 on: August 28, 2018, 09:59:45 PM »
Oh, a frog's eye soup! Nice collection at DeviantArt!

Two more here. The second is a zoom-in of the first.

Offline ThunderboltPagoda

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« Reply #5 on: August 30, 2018, 01:09:49 AM »
Visions of red.

Offline Etymos

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« Reply #6 on: August 30, 2018, 04:35:50 PM »
Those are some very nice pictures. I am currently playing around with Lyapunov maps as well, although I have some trouble with them - and I'm taking a bit of a break hoping I might be inspired to solve it. (Speaking of which, I might have had an idea just now... I'll see if something comes out of it.)

But I have to say, they look good! Lyapunov maps have the ability to look enormously three-dimensional (e.g. the forced logistic map with parts crossing each other).

Offline ThunderboltPagoda

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« Reply #7 on: August 30, 2018, 10:41:30 PM »
Thanks for your response, and good luck for your work with the Lyapunov maps! Yes, with a proper color scheme, Lyapunov images look very three-dimensional. That fascinated me at once when I saw the first examples in Mario Markus' article in Spektrum der Wissenschaft in 1995.

Offline ThunderboltPagoda

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« Reply #8 on: August 30, 2018, 10:54:05 PM »
Two three-dimensional looking Lyapunov fractals (the second a zoom of the first), and an encore.

Offline ThunderboltPagoda

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« Reply #9 on: August 31, 2018, 10:48:05 PM »
Same shape (apart from some stretching), different colors.

Offline ThunderboltPagoda

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« Reply #10 on: September 03, 2018, 10:50:33 PM »
Two more in deep red.

Offline ThunderboltPagoda

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« Reply #11 on: September 04, 2018, 09:04:23 PM »
Lyapunov times four times four

I took one instance of the well known "Lyapunov Space" (sequence ba, a and b in [2, 4]), mirrored it vertically, horizontally, and on both axes, and combined these four images to a large one in four different ways. Here are the first two, #3 and #4 will follow in the next post.

Offline ThunderboltPagoda

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« Reply #12 on: September 05, 2018, 08:53:26 PM »
Lyapunov times four times four, part 2.

Offline ThunderboltPagoda

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« Reply #13 on: September 06, 2018, 03:07:59 PM »
A little joke ...

Offline Caleidoscope

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« Reply #14 on: September 06, 2018, 03:46:41 PM »
:D  funny. 


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