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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > (new) Theories & Research > Bifurcation fractals discovery
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Author Topic: Bifurcation fractals discovery  (Read 9113 times)
Description: Hi res. images and equations of Logistic map etc.
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bkercso
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Posts: 220
« Reply #105 on: July 04, 2015, 01:31:11 AM »
I've made some new zooms, why not. wink It's in delayed, averaged logistic map (fractal=-2 in my program BifFraPl).

Img #32

Set:


Zoom: 3700x, 500 point/pixel, calc. time: 18 min. on 2 CPU-cores



And a newer seen before (neither now grin) hidden bifurcation diagram of it:
(Cannot unhide with more iterations, I tried it.)

Img #33
« Last Edit: July 06, 2015, 10:23:40 PM by bkercso » Logged
bkercso
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Posts: 220
« Reply #106 on: July 06, 2015, 11:52:34 PM »
Img #34 Fine structure of delayed, geometric averaged logistic map.

Set:


Zoom: 1,5x oversampling, 300 points/pixel, 6 min. on 2 cores
« Last Edit: May 20, 2016, 01:33:36 AM by bkercso » Logged
bkercso
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Posts: 220
« Reply #107 on: July 14, 2015, 11:02:03 AM »
I calculated a zoom of roots of double pendulum (of Img #10). It took 1 week.
We can understand these structures if see the video about standard map:
http://www.fractalforums.com/new-theories-and-research/bifurcation-fractal-of-standard-map/

Img #35

Set:


Zoom (empty sections are cutted out; right click for higher resolution), dt=4E-5, dHavg=1E-12, 5 points/pixel:
« Last Edit: May 20, 2016, 01:33:46 AM by bkercso » Logged
bkercso
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Posts: 220
« Reply #108 on: May 20, 2016, 01:35:34 AM »
I unhided the hidden bifurcation map of Img #33!
If you interested how I did it, please visit the Multiple attractor bifurcation fractals topic:

http://www.fractalforums.com/new-theories-and-research/multiple-attractor-bifurcation-fractals/msg92974/#msg92974

The reason of the hidden map is that this chaotic system changed between its chaotic attractors as I stepped the parameter along the horizontal axis.

Img #36: (sorry for low res... embarrass)
« Last Edit: May 22, 2016, 01:32:06 AM by bkercso » Logged
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