Robert made a presentation about a 2-dimensional CA -Langton's Ant- with space filling capabilities. His CA rule generates one single active updating site - updating happens in a very local manner. The behavior reminds me of a 2D Turing machine. Andrew Bragdon did work on space-filling 2D Turing machines at the 2005 NKS Summer School:
Robert showed some nice visual analysis of how often cells in the 2D grid get visited.
Here are three integer sequences that related to his work:
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