Tool

Sierpinski triangle playground

Chaos game on the vertices of a regular polygon. Move halfway (or further / closer) to a random vertex at each step, plot the new point. The classic Sierpinski triangle is 3 vertices, factor 1/2.

Vertices: 3

Step factor: 0.50

Points: 60,000

Chaos game rule

Place 3 vertices V_1, …, V_3 of a regular 3-gon.
Start at any point P_0.
Repeatedly:
  pick a random vertex V_k (uniform over k)
  P_{n+1} = P_n + 0.50 · (V_k − P_n)
  plot P_{n+1}

Similarity dimension: log 3 / log(1/0.50) = 1.5850

render: 0 ms

Sierpinski triangle is the classic case (3 vertices, factor 1/2). With 4 vertices factor 1/2 you get a filled square (each pixel reachable). With 5 vertices factor ≈ 0.382 you get the Sierpinski pentagon (pentaflake without center).

Background at /fractals/sierpinski.

FAQ