## Sierpinski GasketSierpinski
Triangle or Sierpinski Sieve after its inventor
Waclaw Sierpinski. It is produced by the following
set of rules:
- Start with any triangle in a plane.
- Shrink the triangle by ½, make three copies, and translate them so that each triangle touches the two other triangles at a corner.
- Repeat step 2 ad infinitum.
S. Then select
randomly 1, 2, or 3, using a die or some other method. Each random number
defines a new point halfway between the latest point and the labeled point
that the random number indicates. When the game has gone on long enough
the pattern produced is the Sierpinski Gasket. The Gasket has a Hausdorff dimension of log 3/log 2 = 1.585..., which follows from the fact that it is a union of three copies of itself, each scaled by a factor of ½. Adding rounded corners to the defining curve gives a non-intersecting curve that traverses the gasket from one corner to another and which Benoit Mandelbrot called the Sierpinski Arrowhead. ## Related entry• Sierpinski Carpet## Related category• FRACTALS AND PATHOLOGICAL CURVES | ||||||

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