This video shows six different methods of creating the Sierpiński triangle including removing triangles, the chaos game, Pascal's triangle mod 2, the bitwise dominance order, a ternary branching tree, and the arrowhead construction.

0:00 : Six Sierpinski Triangle Constructions
0:09 : Introduction
0:50 : Removing Triangles
1:40 : The Chaos Game
2:53 : Halayudha/Pascal Triangle Modulo 2
4:26 : Ternary Branching Tree
5:00 : Bitwise dominance triangle
7:35 : Arrowhead construction

This is an amazing fractal object that is so fun to think about that I just had to animate these for myself. While I haven't seen the bitwise dominance discussed on YouTube, if you like this video, here are some other fantastic (and better) resources on YouTube for investigating the Sierpiński triangle:

1. @ThinkTwiceLtu's Chaos game :    • Chaos Game | Fractals emerging from c...  
2. @3blue1brown's arrowhead construction from Tower of Hanoi:    • Binary, Hanoi and Sierpinski, part 1   and    • Binary, Hanoi, and Sierpinski, part 2  

And I am sure there are others. You should also check out the wikipedia article for more resources:

https://en.wikipedia.org/wiki/Sierpi%...

The bitwise dominance part (and relatedly the Pascal mod 2 part) is based on the results in this paper by Tyler Ball, Tom Edgar, and Daniel Juda:

https://www.jstor.org/stable/10.4169/...

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#math #manim #visualmath #fractal #sierpinski #pascal #pascaltriangle #arrowheadconstruction #ternarytrees #chaosgame #chaos #triforce #triangle #dynamicalsystems #selfsimilar #iteratedfunctionsystem #mathematics #iteachmath #mathvideo

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Music in this video:
Free Relaxing Chill Music | ARNOR by Alex-Productions |    / @alexproductionsnocopyright  
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Creative Commons Attribution 3.0 Unported License
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