Interactive Lab / The Sierpinski Triangle

Iterated Function System Discovered 1915 Dimension log 3 / log 2 ≈ 1.585

The Sierpinski Triangle

S=f1(S)f2(S)f3(S),fi(x)=x+vi2S = f_1(S) \cup f_2(S) \cup f_3(S), \qquad f_i(x) = \frac{x + v_i}{2}
Cool Fact
The same triangle falls out of Pascal’s triangle: shade every odd binomial coefficient black, every even one white, and the pattern converges to exactly this shape as the number of rows grows. It can also be traced as a single continuous L-system path — see Lab 12, the Sierpinski Arrowhead Curve.

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