Plants, fractals, and formal languages

Although fractal models of natural phenomena have received much attention recently, there are other models of complex natural objects which have been around longer in Computer Imagery but are not widely known. These are procedural models of plants and trees. An interesting class of these models is presented here which handles plant growth, sports an efficient data representation, and has a high “database amplification” factor. It is based on an extension of the well-known formal languages of symbol strings to the lesser-known formal languages of labeled graphs. It is so tempting to describe these plant models as “fractal” that the similarities of this class of models with fractal models are explored in an attempt at rapprochement. The models are not fractal so the common parts of fractal theory and plant theory are abstracted to form a class of objects, the graftals. This class may prove to be of great interest to the future of Computer Imagery. Determinism is shown to provide adequate complexity, whereas randomness is only convenient and often inefficient. Finally, a nonfractal, nongraftal family of trees by Bill Reeves is introduced to emphasize some of the paper's nongrammatical themes.