Limiting patterns produced by substitution systems of the type shown in the previous picture. The patterns on each row are obtained from rules that are set up to give branches with particular relative lengths. The angles between the branches are taken to increase by 15° in successive pictures across the row. Note that pictures shown on different rows are scaled differently—so that the initial vertical stem does not always appear with the same height. The similarity between pictures on this page and overall branching patterns and shapes of leaves in many kinds of plants is striking.

Exportable Images for This Page:

From Stephen Wolfram: A New Kind of Science [citation]