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 [i]Fractal Geometry of Nature[/i]. 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.