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L-Systems, or Lindenmayer systems, are an attempt to characterizing the growth structure of plants formally (mathematically). Lindenmayer started this work in 1968, which coincides more or less (if fuzzy memory serves) with Chomsky’s attempt to do the same with the grammars of natural languages (which ironically was then used by computer scientists to apply it to computer languages)

An L system consists of an alphabet of symbols, an initial string, and a set of rules to convert a symbol in a string to a string. Each symbol represents, typically, a movement forward (like a straight stem growing), a turn right or left, or a step where “context” gets saved and recalled. Let’s look at an example so that this stops being so abstract:

Consider an alphabet of {F, +, -}, an initial state of F, and one rule F -> F+F-F. The L-system develops by applying, at each step, the rules to the current state. In this example, we begin with F, so the first application leads to a new state of F+F-F. Applying the rule of F for every F in that new state gives us the next state: (F+F-F)+(F+F-F)-(F+F-F). I have added parentheses so that it is easier to see where the previous Fs were.