Sierpinski

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Sierpinski
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Drawing the Sierpinski Gasket

• This design is called Sierpinski's Triangle (or
  gasket), after the Polish mathematician Waclaw
  Sierpinski who described some of its interesting
  properties in 1916. Among these is its fractal or
  self-similar character.

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What is a Fractal?

• A fractal is a geometric construction that is
  self-similar at different scales.
• More clearly, a fractal shape will look almost,
  or even exactly, the same no matter what size it
  is viewed at.

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Sierpinski Gasket Algorithm

1. Choose three fixed points T0, T1, T2 to form some
   triangle.

T0
T2
T1
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• 2. Choose the initial point P0 to be drawn by
  selecting one of the points T0, T1, or T2 at
  random.
• Now repeat the following steps until the pattern
  is filled
• Choose one of the three points T0, T1, or T2 at
  random and called it T.
• Construct the next point Pk as the midpoint
  between T and the previously found point Pk-1.
• Pk midpoint of Pk-1 and T
• 5. Draw Pk

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T0
Randomly Selected
T1
T2
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T0
P1
T1
T2
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T0
P1
Randomly Selected
T1
T2
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T0
P1
P2
T1
T2
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T0
P1
Randomly Selected
P2
T1
T2
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T0
P1
P2
P3
T1
T2
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