questions from email - Turing machine/Cellular Automata

Question 1: Analogy of a Turing machine?

Any device which can perform a simile rule set would seem to be an analogy for a Turing’s machine. Computer programs are particularly close because they illustrate a series of operations which are dependent on a group of variables controlled by a user which can provide an unpredicted input into the system causing certain operations or states to happen, and when they are of reasonable complexity they seem to be able to validate ideas or concepts we could not otherwise understand because of their complexity. So in the same way Turing’s machine tried to answer Entscheidungsproblem by building up from a simple series or logical operations, modern computer programs try to answer complex geometrical and logical problems by building up from a series or simple logical operations.

Question 2 Geometrical Aspects of Cellular Automata?

The ability of cellular automata to produce logical understandable patterns, as well as ones of apparent randomness demonstrates that both can be produced from the same simple system. This challenges the idea that randomness can not be logically produced or created, moving the term “random” from something that denotes a process as well as a formation or geometry into a term which can only articulate a product like geometry. With the ends removed logically from its origin, geometry now illustrates something more complicated than a mere representation of logic.