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 : [ Ссылка ]
2. @3blue1brown's arrowhead construction from Tower of Hanoi: [ Ссылка ] and [ Ссылка ]
And I am sure there are others. You should also check out the wikipedia article for more resources:
[ Ссылка ]
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:
[ Ссылка ]
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:
[ Ссылка ]
_________________________________________
Music in this video:
Free Relaxing Chill Music | ARNOR by Alex-Productions | [ Ссылка ]
Music promoted by [ Ссылка ]
Creative Commons Attribution 3.0 Unported License
[ Ссылка ]
