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Substitution Systems and Sequential Substitution Systems

Sequential Substitution Systems involve replacing cells based on neighborhood states, with cells divided into pieces to prevent complexity growth. Explore nested structures, more than 2 states, and disappearing cells to represent real-world scenarios like bio-computing and word processors.

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Substitution Systems and Sequential Substitution Systems

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  1. Substitution Systems and Sequential Substitution Systems

  2. Substitution Systems • On each step, replaces one cell with 0 or more other cells, depending on the state of the neighborhood • Number of cells is not constant, as in CA’s • Depending on rules, may grow exponentially • This gets “unwieldy”

  3. Representations • Cells are still colored blocks • CA: Each Cell is the same size • SS: Cells of the next step are divided into pieces of the previous state, to prevent unwieldiness • Nested Structure • Trees

  4. More complicated… • Systems that rely on more than self state • Rules that allow cells to disappear • More than 2 states • As complex as CAs

  5. Sequential-Ness • So far, the substitutions are in parallel • What if we do it serially? • And what if we had characters instead of blocks? • sequential substitution system

  6. Relation to CAs • Cellular Automata is a subset of substitution systems • If all substitutions are 1 and only one cell • Therefore, they are of the same complexity

  7. Real World: Bio Computing • Word processors • Prolog

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