Six Sierpiński Triangle Constructions (visual mathematics)

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 : https://youtu.be/IGlGvSXkRGI 2. @3blue1brown's arrowhead construction from Tower of Hanoi: https://youtu.be/2SUvWfNJSsM and https://youtu.be/bdMfjfT0lKk And I am sure there are others. You should also check out the wikipedia article for more resources: https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle 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/math.mag.8 If you like this video, please consider liking and subscribing. Also, please comment and share the channel with your friends! :) #math #manim #visualmath #fractal #sierpinski #pascal #pascaltriangle #arrowheadconstruction #ternarytrees #chaosgame #chaos #triforce #triangle #dynamicalsystems #selfsimilar #iteratedfunctionsystem #mathematics #iteachmath #mathvideo To learn more about animating with manim, check out: https://manim.community _________________________________________ Music in this video: Free Relaxing Chill Music | ARNOR by Alex-Productions | https://www.youtube.com/channel/UCx0_M61F81Nfb-BRXE-SeVA Music promoted by https://www.free-stock-music.com Creative Commons Attribution 3.0 Unported License https://creativecommons.org/licenses/by/3.0/deed.en_US