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A level-5 approximation to a Sierpiński triangle obtained by shading the first 2 5 (32) levels of a Pascal's triangle white if the binomial coefficient is even and black otherwise If one takes Pascal's triangle with 2 n {\displaystyle 2^{n}} rows and colors the even numbers white, and the odd numbers black, the result is an approximation to ...
Animated creation of a Sierpinski triangle using a chaos game method The way the "chaos game" works is illustrated well when every path is accounted for.. In mathematics, the term chaos game originally referred to a method of creating a fractal, using a polygon and an initial point selected at random inside it.
The Sierpinski triangle is an n-flake formed by successive flakes of three triangles. Each flake is formed by placing triangles scaled by 1/2 in each corner of the triangle they replace. Its Hausdorff dimension is equal to ≈ 1.585.
English: The Sierpinski triangle is a fractal set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. This diagram of the Sierpinski triangle was generated using an L-system (4 iterations).
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Sierpinski square, a fractal. In 1907 Sierpiński first became interested in set theory when he came across a theorem which stated that points in the plane could be specified with a single coordinate. He wrote to Tadeusz Banachiewicz (then at Göttingen), asking how such a result was possible. He received the one-word reply 'Cantor'.
English: The Sierpinski triangle is a fractal set with the overall shape of an equilateral triangle, subdivided recursively into smaller equilateral triangles. This diagram of the Sierpinski triangle was generated using an L-system (2 iterations).
They are penny graphs (the contact graphs of non-overlapping unit disks in the plane), with an arrangement of disks that resembles the Sierpinski triangle. One way of constructing this arrangement is to arrange the numbers of Pascal's triangle on the points of a hexagonal lattice , with unit spacing, and place a unit disk on each point whose ...