ABSTRACT
By the end of the 1960s, however, it seemed that an alternative might be feasible by refining the formal representation of the rules of growth. Inspired by the intellectual movement dating back to the 1930s that promoted the logical axiomatization of any formal theory in science, a logical and mathematical approach was developed that was initially intended to help explain morphogenesis. When this approach was put into practice, however, it also ended up being in the form of computer simulations, but this time as algorithmic simulations, through formal automata controlled by computer programs. As a result, the biology of shapes would lay claim to another use of com-puters, in particular through the work of Aristid Lindenmayer (1925–1989). Despite some similarities with Dan Cohen’s approach, the type of formalization required by Lindenmayer’s approach was based on a completely different field of theoretical biol-ogy and above all on a completely different interpretation of what mathematization, formalization and theorization meant for biology. Although the embryological and developmental issues that Lindenmayer dealt with seemed close to those of Cohen or Fisher, he did not use the computer in the same way as they had: instead, he sought to avoid any “simulation” in the sense of Cohen’s stochastic realism or Honda and Fisher’s geometric realism. He proposed a form of modelling by automata (later known as L-systems) that would nonetheless increase the possibilities for using computer simulation, and give rise, as we will see, to a decisive controversy regarding “natural formalisms”. How, then, should we view this third type of simulation used in biology (after Cohen’s essentially probabilistic simulation and Honda and Fisher’s essentially geometric simulation) in plant morphogenesis?
