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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. The formula of the scale factor ''r'' for any ''n''-flake is: : where cosine is evaluated in radians and ''n'' is the number of sides of the ''n''-gon. The Hausdorff dimension of a ''n''-flake is , where ''m'' is the number of polygons in each individual flake and ''r'' is the scale factor. 抄文引用元・出典: フリー百科事典『 ウィキペディア（Wikipedia）』 ■ウィキペディアで「N-flake」の詳細全文を読む スポンサード リンク
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