N-flake
Sign in to saveAn '''n-flake, polyflake, or Sierpinski n-gon', 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. Typically, there is also the restriction that the n''-gons must touch yet not overlap.
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15 sectionsContents
- In two dimensions
- Sierpinski triangle
- Vicsek fractal
- Pentaflake
- Hexaflake
- Polyflake
- In three dimensions
- Sierpinski tetrahedron
- Hexahedron flake
- Octahedron flake
- Dodecahedron flake
- Icosahedron flake
- See also
- References
- External links
An '''n-flake, polyflake, or Sierpinski n-gon', 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. Typically, there is also the restriction that the n-gons must touch yet not overlap.
== In two dimensions == The most common variety of n-flake is two-dimensional (in terms of its topological dimension) and is formed of polygons. The four most common special cases are formed with triangles, squares, pentagons, and hexagons, but it can be extended to any polygon. Its boundary is the von Koch curve of varying types – depending on the n-gon – and infinitely many Koch curves are contained within. The fractals occupy zero area yet have an infinite perimeter.