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Author Topic:  Unexpected places to find the sierpinski triangle?  (Read 340 times)

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Offline DeusDarker

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Unexpected places to find the sierpinski triangle?
« on: September 30, 2020, 02:34:55 AM »
Hello! Im currently doing some research for a video on different areas of mathematics and science where sierpinskis triangle pops up. I was wondering if anyone had a suggestion on an unexpected area that it appears in.
So far i have:
  • Pascals triangle mod 2
  • Chaos Games
  • Tower of Hanoi
  • Cellular Automata (Rule 90
  • Burning Ship Fractal
  • Sierpinski Arrowhead Curve
  • Electron arrangement (scientific research)
Thank you! :)

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/unexpected-places-to-find-the-sierpinski-triangle/3794/

Offline TGlad

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Offline marcm200

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Re: Unexpected places to find the sierpinski triangle?
« Reply #2 on: September 30, 2020, 09:26:37 AM »
in DNA when used to compute logical functions (maybe you have this already under electron arrangement):

https://fractalforums.org/share-a-fractal/22/dna-molecules-computing-a-sierpinski-triangle/3232/msg17998#msg17998

Offline lkmitch

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Re: Unexpected places to find the sierpinski triangle?
« Reply #3 on: September 30, 2020, 06:49:07 PM »
It can show up with some logical operations (XOR?). For example,

http://spanishplus.tripod.com/maths/FractalSierpinski.htm

Offline claude

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Re: Unexpected places to find the sierpinski triangle?
« Reply #4 on: October 01, 2020, 12:17:05 AM »
It does not seem to occur cutting the corner off a Menger sponge: https://commons.wikimedia.org/wiki/Category:Menger_sponge_diagonal_section,_stack
I don't know if any fractal antenna use this shape, but maybe...

Offline C0ryMcG

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Re: Unexpected places to find the sierpinski triangle?
« Reply #5 on: October 01, 2020, 04:11:08 AM »
It can show up with some logical operations (XOR?). For example,

http://spanishplus.tripod.com/maths/FractalSierpinski.htm
This one really surprised me! The AND method is remarkably simple. The code just checks if X and Y values equal Zero when ANDed together and color accordingly. The rest is just a quirk of math, I suppose! I'm curious if similar results would work for non-binary equivalents of AND...

I'm sure I've come across Sierpinski Triangles when I wasn't expecting it... usually when I wanted some more unique results and therefore I'd get annoyed about it and not really pay attention to how it got there. But one example I do remember, which might not be exactly what you're looking for, is when I was making a collapsing structure in Minecraft out of sand and torches.
I'd start with a single torch, and placed sand only on top of torches, then placed torches only on the sides of sand where there was only one sand block to chose as the attachment point in that space. (It seemed inelegant to chose one side or the other, so I'd chose neither) So if two sand blocks were separated by only one air, no torch would go there. But if there were three blocks of air between, both sands would get torches on their sides. Soon the familiar triangle took shape.

The fun thing about it is that when you break the bottom torch, the whole thing collapses.

Offline FractalAlex

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Re: Unexpected places to find the sierpinski triangle?
« Reply #6 on: December 20, 2020, 04:48:23 PM »
Well, you can possibly find a Sierpinski triangle in the Perpendicular Burning Ship...
"I am lightning, the rain transformed."
- Raiden, Metal Gear Solid 4: Guns of the Patriots

Offline Lorentzian

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Re: Unexpected places to find the sierpinski triangle?
« Reply #7 on: January 13, 2021, 09:41:14 AM »
For whatever reason the S-triangle likes to pop up in some sea shells! See the picture attached

Offline pauldelbrot

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Re: Unexpected places to find the sierpinski triangle?
« Reply #8 on: January 13, 2021, 05:52:49 PM »
Evidently, there's a row of pigment producing cells along the linear organ that secretes the growing shell at its leading edge, and these cells implement a one-dimensional cellular automaton by having an internal state and exchanging signals with their neighbors. Such cellular automata can often produce Sierpinski patterns. The evolutionary purpose is unclear; it could be accident, or it could be that the patterns afford some measure of camouflage.

Offline Deliberate Dendrite

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Re: Unexpected places to find the sierpinski triangle?
« Reply #9 on: January 13, 2021, 07:02:32 PM »
Not sure if this counts but there's the Eiffel tower.

If not, then there's trusses (roof constructions) based on the sierpinski triangle:
https://www.researchgate.net/publication/271197420_Fractal-Based_Generative_Design_of_Structural_Trusses_Using_Iterated_Function_System/figures?lo=1&utm_source=google&utm_medium=organic


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