B12. WEED

Aristid Lindenmayer was a biologist who lived from 1925 to 1989. He was interested in the mathematical structure of biological organisms, and developed a system for mathematically generating them. Amongst many examples, such L -Systems can be used to generate common weeds similar to the Diffuse Knapweed pictured at left.

Here is an example of the way in which we can generate a weed-like structure. Let F denote a line segment (the ’axiom’). We now use the following ‘production rule’:

                      F F' [+F'] F' [–F'] F'

We assume some appropriate scaling (segment F' is a third the length of F in this case) and an angle = 26° here (say). The production rule is interpreted in the following way. Start with a vertical segment F. Replace it (from the bottom) with a vertical segment F', a similar branching segment F' angled to the left, a vertical segment F', a branching segment F' angled to the right, a vertical segment F'. Now repeat the process, replacing each segment F' in a similar way. The diagram shows the fifth stage in this process, and gives a realistic weed.


Fractals for the Classroom Part 2, Peitgen, H–O., Jürgens, H., Saupe, D. (Springer Verlag 1992)