Image Flocon hexagonal.gif 200px left Image hexaflake.gif thumb right The first six iterations of the hexaflake. Image Cantor cube as hexaflake.gif thumb right Orthogonal projection of a cantor cube showing a hexaflake. A hexaflake is a fractal constructed by Iteration iteratively exchanging each hexagon by a flake of seven hexagons it is a special case of the n flake . As such, a hexaflake would have 7 sup n 1 sup hexagons in its n th iteration. Its Boundary topology boundary is the Koch snowflake von Koch flake , and contains an infinite number of Koch snowflakes black or white . Its Hausdorff dimension is equal to ln 7 ln 3 , approximately 1.7712. It is also the projection of the cantor set cantor cube onto the plane orthogonal to its main diagonal. See also List of fractals by Hausdorff dimension External links http www.walkingrandomly.com ?p 626 Quadraflakes, Pentaflakes, Hexaflakes and more includes Mathematica code to generate these fractals Category Fractals geometry stub ... more details
pentagon third iteration. gallery Hexaflake A hexaflake , or sierpinski hexagon, is formed by successive ... that are scaled by 1 3. The boundary of a hexaflake is the standard Koch curve of 60 degrees and infinitely ... cube onto the plane orthogonal projection orthogonal to its main diagonal is a hexaflake. Like the pentaflake, there is also a variation of the hexaflake that has no central hexagon. Its Hausdorff ... many Koch curves of 60 degrees. gallery File Flocon hexagonal.gif The hexaflake. File Hexaflake.gif The first six iterations of the hexaflake. File Middlemptyhexaflake.png Third iteration of the hexaflake ... of a cantor cube showing a hexaflake. gallery Polyflake n flakes of higher polygons also exist, though ... more details
modulo k ref . math textstyle frac log 6 log 3 math align right 1.6309 N flake Hexaflake Sierpinski ... 3 math align right 1.7712 Hexaflake align center Image Flocon hexagonal.gif 100px Built by exchanging ... more details
Encyclopedia
top
