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The Hypnotic World of Degenerate Spirals

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Re: The Hypnotic World of Degenerate Spirals

#31

Reminds me of Junju Ito’s manga, Uzumaki, a masterful horror piece which involves a town becoming consumed with spirals, anyone else read/seen it?

I really enjoyed the post and yes immediately thought of Uzumaki. I think it’s my favorite thing that he’s done.

Re: The Hypnotic World of Degenerate Spirals

#34

If you like this, you might also like: Belousov-Zhabotinsky reactions https://www.youtube.com/watch?v=PpyKSRo8Iec https://www.youtube.com/watch?v=kw9wF-GNjqs They can form very neat patterns.

Yes you can model it with a diffusion equation.

Re: The Hypnotic World of Degenerate Spirals

#35

Earlier quoted context omitted.

I found this very interesting too, and it actually has a great explanation! Maybe I should have even explored this side a bit deeper in the post itself. Let's say the spiral has rotated 6000 degrees, and I'm approximating it with 100 points (one point every 60 degrees) and line segments. Well, a hexagon is nothing other than 6 points chosen 60 degrees apart from each other at the same distance from a central point, c…

These shapes in the spiral are explored and explained a bit in the classic Tesla spiral hoax too. https://www.conquermaths.com/news/post/index/395/The-Mystery...

Another fascinating video on the prime "arms" in the Ulam spiral.

https://www.youtube.com/watch?v=EK32jo7i5LQ

Re: The Hypnotic World of Degenerate Spirals

#36
post #2

So the degenerate part is taking a fixed sample of points no matter how big the spiral gets. The effect is like you're sampling at larger and larger scales, so you get to sample the structure of the spiral at larger and larger scales, and the diversity of patterns you see, is the visual representation of the spiral at these larger and larger scales through the lens of the sample you are taking. That's my explanation…

Reminds me a bit about a recent blogpost about KSP: https://www.kerbalspaceprogram.com/dev-diaries/6509/. Basically they draw circles as a fixed amount of points as well, but if you zoom enough the circle becomes straight lines. With some work, they're drawing more points on the visible part of the circle as you zoom in.

Re: The Hypnotic World of Degenerate Spirals

#38
post #2

So the degenerate part is taking a fixed sample of points no matter how big the spiral gets. The effect is like you're sampling at larger and larger scales, so you get to sample the structure of the spiral at larger and larger scales, and the diversity of patterns you see, is the visual representation of the spiral at these larger and larger scales through the lens of the sample you are taking. That's my explanation…

Reminds me a bit about a recent blogpost about KSP: https://www.kerbalspaceprogram.com/dev-diaries/6509/ . Basically they draw circles as a fixed amount of points as well, but if you zoom enough the circle becomes straight lines. With some work, they're drawing more points on the visible part of the circle as you zoom in.

In 3D rendering, this is what subdivision surfaces are about. As the camera moves closer, produce more triangles to keep the model appearing smooth. Cool stuff.

Re: The Hypnotic World of Degenerate Spirals

#39

in the spirit of hypnotic -- a while ago I was searching SO on how to animate canvas elements using js. I fell down a bit of a rabbit hole and a few hours later ended up with this: https://codepen.io/867-5309/full/xxqGmVM

Definitely entrancing! Each loop through gave some further interesting shapes. Thanks for posting.

Re: The Hypnotic World of Degenerate Spirals

#40
post #2

So the degenerate part is taking a fixed sample of points no matter how big the spiral gets. The effect is like you're sampling at larger and larger scales, so you get to sample the structure of the spiral at larger and larger scales, and the diversity of patterns you see, is the visual representation of the spiral at these larger and larger scales through the lens of the sample you are taking. That's my explanation…

It's interesting, it's a bit like moire effect due to limited sampling resolution too.. I found the realization pretty profound (as a newb math guy)
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