SIERPINSKI GASKET — CHAOS GAME & IFS
CONTROLS
Mode
Triangle (classic)
Pentagon (5-fold)
Square (r=0.5)
Custom vertices
Restricted (no repeat)
Contraction ratio r:
0.500
Color by:
Last vertex chosen
Orbit history (2 back)
Angle from center
Distance from attractor
Points per frame:
1000
Clear & Restart
Pause
POINTS DRAWN
0
FRACTAL DIMENSION
—
IFS MAPS
3
Chaos Game (Barnsley 1988):
Pick a random vertex. Move halfway toward it. Plot. Repeat.
Equivalent to iterating a random IFS contraction. The attractor is the Sierpinski triangle.
d_f = log(3)/log(2) ≈ 1.585
Coloring by orbit history
reveals the self-similar structure: each color corresponds to a different sub-triangle in the IFS hierarchy.