Dragon Curve fractal

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bwisialo
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Dragon Curve fractal

Post by bwisialo » Thu Feb 11, 2016 1:21 pm

This blows my mind more than the Koch snowflake or the lattice structures. Just... wow... unbelievable! I'd been tinkering with patterns that kind of sort of looked a bit like dragon curves. But this is an honest to goodness, actual dragon curve!! :D

Image

1024 cells
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A dragon curve is made up of smaller dragon curves.
Image

The 256-cell curve below occurs 2 iterations earlier than the one above, and the curve above is made up of 4 of them put together.
Update: Look here to see how the 4 smaller curves fit together to make the larger one.
Image
amor fati
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Alast
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Re: Dragon Curve

Post by Alast » Thu Feb 11, 2016 3:23 pm

Amazeballs!!! You've become a Cell Lab Artist!
Perfection hasnt reached me yet, but its trying hard!
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Alast
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Re: Dragon Curve

Post by Alast » Fri Feb 12, 2016 7:27 pm

Hey buddy,

I'm not quite sure how to say it, but I was tinkering with 1 mode fractals... and see what suddenly came out:

Image
Perfection hasnt reached me yet, but its trying hard!
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Fri Feb 12, 2016 9:00 pm

That's awesome! :D From the way the curve Is constructed mathematically, 1 mode makes perfect sense, but I couldn't get it to work. Mine gets messy if I try to do 4096.
amor fati
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Alast
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Re: Dragon Curve

Post by Alast » Fri Feb 12, 2016 9:16 pm

So does mine. I can't make a petri dish large enough to actually work for that.

I experimented further with 1 mode fractals. Some interesting shapes are possible but as can be expected, the possibilities are a little limited. The Dragon Curve is definitely the most impressive one.
Perfection hasnt reached me yet, but its trying hard!
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Fri Feb 12, 2016 9:40 pm

Oh, right, I actually do have the 1 mode version, but I like my final mode to be Lipocytes. So, I have a mode 2 Photocyte with the same angles as mode 1.

On another note, the 64 cell limit in the preview animation can be a serious limitation on being being to have a good sense of what the result is going to be. Would be nice if the animation went up to, say, 512. That shouldn't be a problem -- maybe in the next release ;)
amor fati
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Fri Feb 12, 2016 9:46 pm

PS - Oh, right... Part of the reason I use Lipocytes is size. If you make your last mode a Lipocyte, you'll have enough room to produce a 4096 dragon curve. I think I used 8 or 10mm.
amor fati
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Fri Feb 12, 2016 9:50 pm

It might be possible to do 4096 by producing 4 of the dragon curve initial cells in a square. I haven't tried that yet.
amor fati
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Fri Feb 12, 2016 10:26 pm

Here's my 2-mode genome for the Dragon curve. The next step is to get it to reproduce the pattern correctly at 4096. Well, it produces the pattern, but too many cells have adhesins where the swirls meet up, distorting them.

You'll have to create a substrate with the cell limit where you want the genome to stop. You'll have to adjust viscosity: eg, start low, then none, then very low.

https://www.dropbox.com/s/7h6pv9gzmtisd ... enome?dl=0

Mode 1: Lipocyte, split mass 0.77, split angle 45, splits into child modes 2, 2
Mode 2: Photocyte, split mass 2.92, split angle 45, splits into child modes 1, 1

both:
max adhesion strength
max nutrient priority

You'll have to create a substrate with the cell limit where you want the genome to stop. You'll have to adjust viscosity: eg, start low, then none, then very low.
amor fati
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bwisialo
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Re: Dragon Curve

Post by bwisialo » Sat Feb 13, 2016 4:07 pm

PS - I oriented the arms turning "clockwise" to match the traditional dragon curves, but I think counter-clockwise may help it unfold better at larger scales. The collective but slight propulsion from cell splits creates a very slight "spin," and the arms can get caught up with other cells as they propagate and unfold.
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