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Attractive snowflake-like designs can be created by iteratively arranging -gons around an initial -gon. A famous example of such a construction is the pentaflake, which was first noticed by Albrecht Dürer. This Demonstration allows you to experiment with several different types of -flakes. The "scale factor" slider only affects -flakes of the type "variation 2" and controls the relative size of the secondary -gons.

Contributed by: Michael Croucher (March 2011)
Based on a program by: Eric W Weisstein
Open content licensed under CC BY-NC-SA



Snapshot 1: the first iteration of the standard pentaflake construction

Snapshot 2: the fourth iteration of the standard pentaflake construction

Snapshot 3: the first iteration of the hexaflake construction

Snapshot 4: the fifth iteration of a variation on the standard pentaflake construction. Whereas the standard pentaflake construction uses identical pentagons throughout, this variation uses scaled pentagons for each iteration.

Snapshot 5: a similar construction to the pentaflake is this, the Vicsek fractal, which is constructed from squares rather than pentagons. This is the fourth iteration of the Vicsek fractal.

Snapshot 6: a snowflake constructed using scaled hexagons

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