Below, we see the first six levels of the Koch Snowflake -- that is, the starting point (the equilateral triangle) along with the first 5 steps obtained by following the defining recursive rule.

The Koch Snowflake exhibits symmetry of scale -- no matter how much we zoom in, we alwalys see the same level of complexity, or of detail.

Below, we see an animation of zooming in continuously on one third of the Koch Snowflake (this portion can be created on its own by applying the recursive rule just to a line segment; it is known as the Koch Curve):





Developing the Sierpinski Triangle
The Sierpinski Triangle

Illustrating the number of pieces we break one "side" of the Koch snowflake into, and the scale factor for the Koch Snowflake:

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