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The time-space diagram of a replicator pattern in a cellular automaton also often resembles a Sierpiński triangle, such as that of the common replicator in HighLife. [9] The Sierpiński triangle can also be found in the Ulam-Warburton automaton and the Hex-Ulam-Warburton automaton.
An n-flake, polyflake, or Sierpinski n-gon, [1]: 1 is a fractal constructed starting from an n-gon. This n-gon is replaced by a flake of smaller n-gons, such that the scaled polygons are placed at the vertices, and sometimes in the center. This process is repeated recursively to result in the fractal.
The Koch snowflake (also known as the Koch curve, Koch star, or Koch island [1] [2]) is a fractal curve and one of the earliest fractals to have been described. It is based on the Koch curve, which appeared in a 1904 paper titled "On a Continuous Curve Without Tangents, Constructible from Elementary Geometry" [3] by the Swedish mathematician Helge von Koch.
The diagram shows the construction on an IFS from two affine functions. The functions are represented by their effect on the bi-unit square (the function transforms the outlined square into the shaded square). The combination of the two functions forms the Hutchinson operator. Three iterations of the operator are shown, and then the final image ...
Koch snowflake; L-system; Lévy C curve; ... but a diagram showing how the elements meet. Tessellations ... Sierpinski triangle ...
Sierpinski Hexagon: Built in the manner of the Sierpinski carpet, on an hexagonal grid, with 6 similitudes of ratio 1/3. The Koch snowflake is present at all scales. (+) 1.6379: Fibonacci word fractal: Fractal based on the Fibonacci word (or Rabbit sequence) Sloane A005614.
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).
Mosely snowflake formation during four recursion steps Mosely snowflake (heavier) formation during four recursion steps. The Mosely snowflake (after Jeannine Mosely) is a Sierpiński–Menger type of fractal obtained in two variants either by the operation opposite to creating the Sierpiński-Menger snowflake or Cantor dust i.e. not by leaving but by removing eight of the smaller 1/3-scaled ...