The full array of patterns that can be produced by simple substitution systems in which each stem branches into exactly two symmetrical stems at each step. The patterns are arranged on the page so that the pattern shown at a particular position corresponds to what is obtained with a rule in which the tip of the right-hand stem goes to that position (corrected for the aspect ratio of the array) relative to the original stem shown as a vertical line on the left-hand side of the page. In each case the result of 10 steps of evolution is shown, and the pictures are scaled so that all points above the bottom of the original stem can be included. Note that for rules outside of a distorted semicircle centered on the dot at the left-hand side of the page, and touching the three other sides of the page, the patterns generated grow at each step, rather than tending to a limit of fixed size.
Showing Web View For Page 406 | Show full page with images