This Wolfram Summer School project is an attempt to represent a system subject to a potential using Circular-String Rewriting Systems. Circular strings have the property of being oriented, and the characters in the string have only relative position. This property can be used to apply String Rewriting Rules at the boundary of a string. The graphs of CSRS are often much smaller than the graphs for SRS because rules can apply in more positions, since orientation is the only spatial constraint. Reducing the number of states in a system with similar amounts of rewriting events leads to a multiplicity of causal edges leading to each state. Such simple systems offer an opportunity to investigate the proposed identification in the Wolfram Model that the energy of a system can be represented by a flux of causal edges through a spacelike hypersurface, in this case it is potential energy represented. One possibility of extending this idea to a Quantum system is that the higher-order combinatorics of "Classical" rewrite rules make transitions between states that are resolved with few iterations.
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