Chapter 8: Implications for Everyday Systems

Section 6: Growth of Plants and Animals

History of branching models

The concept of systematic rules for the way that stems—particularly those carrying flowers—are connected in a plant seems to have been clearly understood among botanists by the 1800s. Only with the advent of computer graphics in the 1970s, however, does the idea appear to have arisen of varying angles to get different forms. An early example was the work of Hisao Honda in 1970 on the structure of trees. Pictures analogous to the bottom row on page 402 were also generated by Benoit Mandelbrot in connection with his development of fractals. Starting in 1967 Aristid Lindenmayer emphasized the use of substitution or L systems (see page 893) as a way of modelling patterns of connections in plants. And beginning in the early 1980s—particularly through work by Alvy Ray Smith and later Przemyslaw Prusinkiewicz—models based on L systems and fractals became routinely used for producing images of plants in practical computer graphics. Around the same time Michael Barnsley also used so-called iterated function systems to make pictures of ferns—but he appears to have viewed these more as a curiosity than a contribution to botany. Over the past decade or so, a few mentions have been made of using complicated models based on L systems to reproduce shapes of specific types of leaves, but so far as I can tell, nothing like the simple model that I describe in the main text has ever been considered before.

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