Inward Curve fractals

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bwisialo
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Inward Curve fractals

Post by bwisialo » Wed Feb 24, 2016 1:42 am

"Inward curve" isn't a technical category -- it is merely a description of the sorts of fractals below. The ideal type that I'm aiming to create are patterns with similarities to the "Levy C curve" fractal. Here is the eighth iteration of the fractal.
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Successive iterations give rise to greater complexity in the bottom center first, and then replicate themselves up the sides to the top. The final patterns below do exactly that. Unfortunately, their complexity makes them incredibly difficult to produce with a high number of iterations / cells. All these fractals are generated from two modes.

Here is a basic pattern whose first iterations have minimal differences between the bottom, side, and top. But even small differences get compounded. By the iteration in the first image, the bottom center of the curve is slightly more complex than the side, which is slightly more complex than the top. A couple iterations later, the bottom center is much more complex, in the second image. The second structure is 4096 cells and somewhat close to reaching equilibrium where adhesins and cells come to rest and the full pattern reaches its final form, but it is at 250 hr and is about to die.
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Patterns that begin with greater complexity exhibit significant differences between the bottom and sides much earlier. Also see the final images below.
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The orientation of the pattern's most basic components matters: here, the orientation results in the sides having the greatest complexity, which is another direction to take fractals.
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Most of the patterns I created are angular, but rounded versions are possible. Here again, greater complexity developing in the bottom center of the curve.
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Below are the patterns that seem to be the most similar to the sort of curve develop seen in the Levy C curve, though none of them are approximation of that particular curve. The first and second are very similar, but the first has slightly different angles that produce greater self-similarity and a more intricate and complex pattern. The first and third have been extremely difficult to produce with at a high number of iterations / cells (Update: see the next post for representations of the first and third patterns). I managed to get a well-developed version of the second pattern.
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4096 cells
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amor fati
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Wed Feb 24, 2016 5:39 pm

I was able to get a relatively well developed version of the last pattern in the previous post. :) Compare to the level of development in that post.

4096 cells
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Bottom:
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Middle-right and bottom-right:
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Middle-right and upper-right:
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amor fati
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Wed Feb 24, 2016 11:33 pm

And... I was also able to produce a well-developed, high-cell count version of the first of the final three patterns in the initial thread post. :)

2048 cells
Image
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Alast
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Re: Inward Curve fractals

Post by Alast » Thu Feb 25, 2016 8:54 am

Nice ones :) I always struggle with high cell counts when they're only connected at 1 point. So much that I tend to give up on them. Glad you've managed well :)
Perfection hasnt reached me yet, but its trying hard!
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Thu Feb 25, 2016 10:50 pm

Thanks Alast. :) I like them quite a bit as well.

Here's an example of combining different sorts of iterative patterns, creating an inward curve of lattices. The are subsequent iterations.
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Tue Mar 29, 2016 5:47 pm

Oh, interesting. These are "binary tree" fractals -- at least some of them are. They represent the "branch tips" of a tree created by repeatedly splitting Left and Right at a fixed angle, like this

Image

Different angles yield different patterns. I might have to return to these and do some exploring.
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CandyYAHFT
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Re: Inward Curve fractals

Post by CandyYAHFT » Tue Mar 29, 2016 7:03 pm

Wow there are too many cells, too much that the thing set me doubts abou it being legit, you are an artist that uses the genome editor as your pen
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Tue Mar 29, 2016 7:30 pm

And... if the angle is 45, the result is the Levy curve. I wasn't totally off base after all. ;)
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bwisialo
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Re: Inward Curve fractals

Post by bwisialo » Tue Mar 29, 2016 7:35 pm

Yes, these are unwieldy and gangly with so many cells. I wanted to see as many iterations as possible, but I need to cut the cells back to get the structure to reach equilibrium / final form... unless Petter makes infinite lifespan an option on experimental plates. ;)
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Re: Inward Curve fractals

Post by CandyYAHFT » Tue Mar 29, 2016 8:31 pm

I tough salinity did that, but my mistake, they die anyway :oops:
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