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The following is an attempt to acquaint the reader with a fractal object called the Sierpinski gasket. The gasket was originally described in two dimensions but represents a family of objects in other dimensions.
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local.wasp.uwa.edu.au/~pbourke/fractals/gasket/
local.wasp.uwa.edu.au/~pbourke/fractals/gasket/
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Oct 27, 2009 ... It is also called the Sierpiński gasket or Sierpiński triangle. The curve can be written as a Lindenmayer system with initial string ...
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mathworld.wolfram.com/SierpinskiSieve.html
mathworld.wolfram.com/SierpinskiSieve.html
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The Sierpinski gasket is also referred to as the Sierpinski triangle or as the Sierpinski triangle curve. ... We remove "all" of the area of the initial triangle in constructing the Sierpinski gasket. But of course there are many points still left in the gasket.
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ecademy.agnesscott.edu/~lriddle/ifs/siertri/siertri.htm
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This means that we have removed "all" of the area of the original triangle in constructing the Sierpinski gasket. But of course there are many points still left in the gasket. That is one reason why area is not a useful dimension for this set...
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ecademy.agnesscott.edu/~lriddle/ifs/siertri/area.htm
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Sierpinski Gasket and Tower of Hanoi, proof of Lucas' Theorem ... As was discovered by Ian Stewart, puz(Tower of Hanoi) has a surprising relationship to the Sierpinski gasket (also known as the Sierpinski triangle) and, therefore, to Pascal's triangle.
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www.cut-the-knot.org/triangle/Hanoi.shtml
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Many ways to create the Sierpinski Gasket ... Dot Patterns and Sierpinski Gasket ... So, how many ways are there to define the Sierpinski gasket (also, the Sierpinski triangle)? I counted a respectable 11 but undoubtedly there are more. I would be happy to be advised of additional ones.
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www.cut-the-knot.org/ctk/Sierpinski.shtml
www.cut-the-knot.org/ctk/Sierpinski.shtml
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The Sierpinski Gasket is named for the Polish mathematician who first proposed it. It is a fractal image that is made from equilateral triangles. A Sierpinski Gasket can be easily constructed by anyone who can manage paper, scissors, and glue.
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wwwc3.lanl.gov/mega-math/new/sierpins/sierpins.html
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The Sierpinski Gasket a triangle with the center triangle cut out of each solid triangle recursively. It can be shown that the triangle has no area. This image can be generated in many ways.
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home.steuber.com/sarah/Java/Sierpinski/Sierpinski.html
home.steuber.com/sarah/Java/Sierpinski/Sierpinski.html
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How might we coerce our turtle into making a Sierpinski gasket? While the procedure is simple enough to describe, explicitly writing it down in symbols requires a bit of thought. Give it a try before continuing.
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www.math.sunysb.edu/~scott/Book331/Sierpinski_gasket.ht...
www.math.sunysb.edu/~scott/Book331/Sierpinski_gasket.html
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