Koch Snowflake Curve
In each iteration step every segment is replaced by four segments of equal length, the new length is one third of the previous segment length. The animation shows 5 iterations. The Koch Snowflake is infinite iterations.
The animation shows how the iteration construction can be varied. We continue to replace each segment by four shorter segments. The new length varies between 1/4 and 1/2 times the old length.
Each frame shows the limit curve of snowfake with different parameter shown in “snowflake_varyconstruct_001”. (actually, each shows the 5th iteration.) Observe that their Hausdorff dimension changes from 1 to 2.
Escher Snowflake is a variation of korch snowflake. We start with a configuration of “tiles” that tiles the plane. Each tile is a polygon. We replace each edge of polygon by a zigzag, in such a way that the polygons remain congruent.
Escher Snowflake with 7 iterations.
the limit curves of Escher snowflake with different parameters. Observe that their Hausdorff dimension changes from 1 to 2.