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Sierpiński triangle

2015-07-18, post № 47

mathematics, programming, Pygame, Python, #3, #3-gon, #around the center, #black, #black and white, #fractal, #generates, #generating, #generator, #three, #triangle, #white

Having recently heard something about chaos theory, I was interested in the Sierpiński triangle. Specifically in the random generation. To prove that it can really be generated using a die, I wrote this program.

How it works

  • You start with any point inside the triangle (I chose the center).
  • A triangle has three points, let us call them 𝐴, 𝐵 and 𝐶.
  • You choose randomly between one of those three points, go half the distance and set a pixel right there.
  • Repeating this process over and over again (always starting at your last point), you eventually [1] get the Sierpiński triangle.

Controls

  • ‘Space’ toggles if the triangle is generated,
  • ‘m’ toggles if the current position is shown (indicated by a blue circle).
sierpinski-triangle-1.png
sierpinski-triangle-2.png
sierpinski-triangle-4.png
Source code: sierpinski-triangle.py

Footnotes

  1. [2020-07-08] This post in particular was slightly edited to better reflect current standards. A note one may add is that “eventually” should really say “in the limit”, as no finite amount of time will lead to the true fractal using the described methodology.
Jonathan Frech's blog; built 2022/05/14 19:35:56 CEST