Peano Curve in Snowflake
- Michael Ortiz
This shows the first five steps in the generation of a Peano curve that fills the Koch snowflake. At each stage the figure shown consists of a single open, simply connected polygonal curve. In principle the entire thing can be traced on paper without lifting one's pencil or crossing a line, beginning at the lower left-hand point of the star and ending at the lower right-hand point. The seven-interval generator may be viewed by moving the slider to the left. This curve was designed by Benoit Mandelbrot and described in his Fractal Geometry of Nature. Please view my teragon applet to see the figure that results when we "fill in" one of the two regions into which the curve separates the snowflake.