Context Free L-Systems

Consider the simplest type of L-system namely, a deterministic context-free L-system, also called a DOL-Systeni. As the name implies, the production rules of such systems are allowed to transform only single symbols i.e. the dynamics is independent of all neighboring symbol values. DOL-Systems are thus generalized CA systems that are allowed to add sites but whose local rule depends only on a given site itself and none of its neighbors. 

As a simple example, suppose that A consists of three elements, a = 0, 02 = 1, and — 2 and there are three production rules 7 [0] 21, 7 [1] 0 and 

7 [2] 01. Starting from the axiom q(0) = 0, the first few symbol strings are then 

From this first example, it is obvious that, apart from a CA-like pai allel updating of an ever-increasing number of sites and the set of recursive symbol-strings to which such a dynamics inevitably leads, there is no real internal geometry, as such. Each string at time t remains essentially a static collection of abstract symbols. 

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