Inward Curve fractals

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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Tue Mar 29, 2016 9:07 pm

The only workaround I've thought of -- but I haven't tried it -- is to start without Nitrates, then let the initial structure get into place. Very briefly introduce nitrates, then take them away, and when reproduction stops, let the structure get into place. Etc. That way, you wouldn't have to rely only on the lifespan of the final cells produced in order to reach equilibrium.
amor fati
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Tue Mar 29, 2016 10:17 pm

I got some very cool results, one of which brings these binary trees back around to the Koch curve. It's crazy the different ways fractals are related to one another.
amor fati
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Tue Mar 29, 2016 10:39 pm

And... the golden ratio makes an appearance! :D Will post later.
amor fati
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Wed Mar 30, 2016 12:59 am

The structure is not 100% in it's equilibrium position, but I think you'll get the idea. The branching angle here is 60 degrees -- one left, one right, with 120 degrees between them. The black and red branches below: 1st branch right, and 2nd branch left. The branches cut through the midpoints of the structure. With 60 degree branching, the ratio between successive branches is the golden ratio: if red branch = 1, then black branch = (1+ sqrt 5) / 2 = 1.618.... And, for what its worth, the central angles are the elusive 60 degrees -- though you can't make a triangle from them.

Image

Image
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Wed Mar 30, 2016 6:41 pm

One of the cool things here is that Alast and I had already posted several of these. Alast posted the right triangle (which is a binary tree branching at 135) and "clubs" (whose alternate iteration is a binary tree of I believe 150 based on available Snap values -- very similar to 140 below). I posted a 75 degree binary tree and, later, a 60 degree one. Alast posted what I believe is a 105 degree tree based on Snap values, very similar to 108 below.

(Another cool thing is that the genomes match the branching angles, and in a fairly intuitive way. You can use the Split angle and Child 2 split angle to produce the binary trees. For a 75 degree tree, Split angle is 75. To figure out Child 2 angle: 360 – (2 * 75) = 210. Here's how it works out: Child 1 splits at 75 and Child 2 now splits at 285 -- that is, the two children split 0 +/- 75 respectively.)

This all makes a nice full circle. In the super short, super cool video at bottom, you'll see the examples that have been posted and everything in between in a continuous flow, from 0 to 180 degrees. You'll see the "inward curve" patterns up to the 90 degree block; then obtuse angled trees, with the right triangle at 135 and Koch curves after that.

45 - similar to Levy curve

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108 has a golden ration between successive branch lengths

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120 also gives a golden ratio

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140 (144 gives a golden ratio but 140 is a tighter triangle)

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https://youtu.be/M7Fy_kXbOfc
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