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Fractal Dimension versus Process Complexity
2016
Advances in Mathematical Physics
We look at small Turing machines (TMs) that work with just two colors (alphabet symbols) and either two or three states. For any particular such machineτand any particular inputx, we consider what we call thespace-timediagram which is basically the collection of consecutive tape configurations of the computationτ(x). In our setting, it makes sense to define a fractal dimension for a Turing machine as the limiting fractal dimension for the corresponding space-time diagrams. It turns out that
doi:10.1155/2016/5030593
fatcat:g6ptxsbn3jfqfaaayeedmk7twm