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Welcome to Fractal Forums > Fractal Math, Chaos Theory & Research > General Discussion > Transforming one bud into another
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Author Topic: Transforming one bud into another  (Read 2090 times)
Description: Does anyone have an idea how to do that?
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makc
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« on: March 30, 2010, 11:47:21 AM »
Few days ago I was recreating this in hopes to make an animation, but it turns out that changes get too subtle after 50th frame or so. Still, I think an interesting animation could be made if anyone finds a way to build interframes with unfolding branches for those 1st 50 frames (attached animation is fake made in winmorph just to give better idea of what I am talking about). The problem is, this is equivalent to finding smooth coordinates transform between two buds, which is a job for math genius like YOU smiley so I am posting it here. In case anyone have an ideas...
* 1.avi (42 KB - downloaded 150 times.)
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bib
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« Reply #1 on: March 30, 2010, 11:55:52 AM »
Interesting animation. With a more basic approach I did this one a while ago:
<a href="http://www.youtube.com/v/ULHZjnCp99c&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/ULHZjnCp99c&rel=1&fs=1&hd=1</a>
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makc
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« Reply #2 on: March 30, 2010, 12:01:31 PM »
exactly what I am talking about, ~20th second and onwards there is virtually no difference.
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Timeroot
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« Reply #3 on: March 30, 2010, 05:41:43 PM »
I think you might want your branch number growing faster - not linearly. Just take which ever parameter in the formula that represents the branch number, and replace it with exp(BranchNumber). You can also try cubic growth, or tangent growth - it would take you to infinite bulb number in finite time. Good luck, and let us see the anim once it's done!  cheesy
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makc
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« Reply #4 on: March 30, 2010, 06:29:56 PM »
Quote from: Timeroot on March 30, 2010, 05:41:43 PM
I think you might want your branch number growing faster - not linearly.
Yes I tried that (used fibonacci sequence) but this has a problem of max iterations needed to render this growing exponentially, and no significant diversity improvement within 1st 20 frames.
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Timeroot
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« Reply #5 on: March 30, 2010, 06:57:20 PM »
One interesting thing you could do is cycle between the different n-period buds. That is, the 1/23 bud, 2/23, 3/23, 4/23, 5/23, 6/23... 12/23. It might actually be more diverse than changing the denominator.
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Someday, man will understand primary theory; how every aspect of our universe has come about. Then we will describe all of physics, build a complete understanding of genetic engineering, catalog all planets, and find intelligent life. And then we'll just puzzle over fractals for eternity.
makc
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« Reply #6 on: March 30, 2010, 10:49:56 PM »
This way they should not branch, just wind into spiral, not sure if that also converges to identical image... But I have no general-case formula to try it out - help?
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