Quote:
Originally Posted by ceptimus
But (in Life) we could run two grids side by side. One could be full of gliders - lots of action - and then eventually settle down to a static pattern. The second grid could just be that static pattern from the start. Are you really claiming that these two 'Life universes' are equivalent?
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Yes, but they are equivalent in all respects to the Conway's life system. That we can
see a more complicated version of one (non stable) is dependent on the fact that we have the ability to pause and suspend the rules.
Thus a blue square in the center of grey squares simply hasn't been
figured out yet to actually be a grey square. Its suspended because the interactions of a large grid have an extremely complicated total solution. But, for instance, a grid as large as the rule itself, like the (grid of 9 squares one in the middle is blue) is another way of saying what it equals, not what happens next. It only matters "what happens next" if what happens next is some sort of interference such that it is no longer surrounded by grey squares. But because the
entire grid is just these nine squares, no glider or anything is going to interfere.
Essentially what it boils down to is you could right a rule for the entire initial state of the grid, and that rule would be consistent with every rule of Conway's life.