#### Two-Space Cellular Automaton Polymer

*by Gavin Crooks, August 1997*

This a Java simulation of a simple model polymer. Considering the monomers to be numbered sequentially along the chain, we separate them into even and odd sets. The odd and even monomers are located on 2 separate 2-dimensional square lattices. Only the even monomers are shown above. Even monomers directly interact only with odd monomers and vice versa. Two monomers are considered connected if they lie in opposite spaces within 1 square of each other. Note that monomers in opposite spaces can lie on top of one another.

The polymer is moved as follows. A monomer (from either even or odd spaces) and a direction to move (North, South, East or West) are chosen at random. The move is accepted only if it does not change the connectivity of the polymer chain. In the diagram below, if the monomer moves as shown then the six shaded squares must be empty in the opposite space. If the squares on the left are not empty then the move would break the chain. If the squares on the right are not empty then the move would result in a new monomer-monomer link. Excluded volume is also preserved as monomers in the same space are prevented from moving on top of each other.

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| | # | | | | # |
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| | # | O-+-> | | # |
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| | # | | | | # |
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All monomers in one space can be moved simultaneously, and the movement algorithm is local, so this simulation qualifies as a Monte Carlo simulation and as a stochastic Cellular Automaton.

For further information see Y. Bar-Yam, Y. Rabin, M. A. Smith, *Macromolecules Rep. , ***25** (1992) 2985.