“snowflake_iterate_001”
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.
“snowflake_varyconstruct_001”
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.
“snowflake_varylimit_001”
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
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.
