How a 1-Dimensional Fractal Generates 2-Dimensional Fractals #SoME3

I have been wanting to make a video for SoME since the first one, but never got around to it. Now I have. Hope you enjoy! :D Special thanks to ‪@3blue1brown‬ for running SoME Timestamps: 0:00: Intro 0:33: Number bases (feel free to skip this portion) 3:52: The Cantor Set 10:12: Devil's Staircase 11:44: Menger Sponge 13:55: Sierpinski Triangle 15:55: Conclusion Thanks to -minushypen1two379 in the comments for the help! Errors: 4:15: The labels for the numbers at 7/9 and 8/9 are incorrectly labeled as 3/9 and 4/9. 11:34: I say that the Devil's Staircase has a derivative of 0 everywhere. This is untrue. It has a derivative of 0 almost everywhere. On the other hand, it is continuous everywhere. The Menger Sponge is actually the 3D version of the 2D Sierpiński Carpet. Resources Wikipedia Number Bases: https://en.wikipedia.org/wiki/Radix Cantor Set: https://en.wikipedia.org/wiki/Cantor_set Devil's Staircase: https://en.wikipedia.org/wiki/Cantor_... Menger Sponge: https://en.wikipedia.org/wiki/Menger_... Sierpiński triangle: https://en.wikipedia.org/wiki/Sierpiń... Websites More on Number Bases (on Maths is Fun): https://www.mathsisfun.com/numbers/ba... Videos Comprehensive Number Bases Playlist (by Oninab Resources):    • Number Bases   More on the Cantor Set (by Zach Star):    • What happens at infinity? - The Cantor set   More on the Cantor Set (by Michael Penn):    • journey into fractals: the Cantor set and ...   More on the Devil's Staircase (by PBS Infinite Series):    • The Devil's Staircase | Infinite Series   More on the Menger Sponge and also a big inspiration for this video (by Matt Parker):    • The Fractal Menger Sponge and Pi   More on the Sierpiński Triangle (by Numberphile):    • Chaos Game - Numberphile   How to generate the Sierpiński Triangle from Pascal's Triangle (by Eddie Woo): Sierpiński Triangle Editing Software: VSDC Microphone: My Phone Animation Software: Aseprite Grid Size: 256x144