1 jan 2010
- Koch pentaflake
The construction of this snowflake is similar to the usual Koch hexaflake.
Start with a pentagon, or the first pentaflake
and divide the original edges in four smaller ones, as indicated in the second pentaflake.
The new edges make angles of 108°, 36° and 108° respectively and their length is 0.381966 = *:θ times the original edge length, where 0.618033 = θ =: -: <: %: 5 .
Notice that this division of edges is similar to the division of the (base of the) triangle in Penrose-like Tiling.
The Hausdorff dimension is then equal to 1.44042 = - 2 %&^. θ . This is equal to with =72°, in list of fractals by Hausdorff dimension.
- Koch pentastarflake
is another snowflake with the same construction and the same Hausdorff dimension:
It comes from