Recursive growth models

It was mentioned at the outset that L-systems were designed as tools for modeling filamentous plants. Since, as we have just seen, there is no real intrinsic structure or geometry in L-systems, a plant may be given some semblance of physical structure only by an appropriate graphical re-interpretation of a somewhat souped-up alphabet. 

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Given the nonlinearity of recursive growth, predicting the aggregate differences (or lack thereof) resulting from model-level decisions is very difficult, perhaps impossible. Considering the breadth of models currently existing in AE, empirical comparison on an accepted test problem should prove valuable. 

Our main concern here is the dynamics of these molecule numbers A, of the species i in relationship with the condition of the recursive growth of the (proto)cell. In our model there are four basic parameters the total number of molecules N, the total number of molecular species k, the mutation rate p, and the reaction path rate p. By carrying out simulations of this model (choosing a variety of parameter values N, k, p, and p) and also by taking various random networks, we have found that the behaviors are classified into the following three phases [32,33] ... 

Macosko and Miller (1976) and Scranton and Peppas (1990) also developed a recursive statistical theory of network formation whereby polymer structures evolve through the probability of bond formation between monomer units this theory includes substitution effects of adjacent monomer groups. These statistical models have been used successfully in step-growth polymerizations of amine-cured epoxies (Dusek, 1986a) and urethanes (Dusek et al, 1990). This method enables calculation of the molar mass and mechanical properties, but appears to predict heterogeneous and chain-growth polymerization poorly. 

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