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But as soon as the density is increased above 50%, regions of black progressively expand, eventually taking over the whole system. … The rule is set up so that whenever a region of black occurs to the left of a region of white, an expanding region of gray appears in between. … And when this happens, the black expands and the gray gradually tapers away.
The pattern produced continues to expand on both left and right, but only the part that fits across the page is shown here.
Note that the particular rule used here yields a pattern that expands on the left but not on the right.
Note that the pattern shown here has been truncated at the edge of the page on the left, although in fact the whole pattern continues to expand to the left forever with an average slope of Log[2, 3]≃1.58 .
The pattern continues to expand on the left forever, but only the part that fits across each page is shown.
The pattern continues to expand on the left forever, but only the part that fits across each page is shown.
The pattern continues to expand on the left forever, but only the part that fits across each page is shown.
The pattern continues to expand on the left forever, but only the part that fits across each page is shown.
The pattern continues to expand on the left forever, but only the part that fits across each page is shown.
In the expanded tag system evolution, successive colors of elements are encoded by having a black cell at successive positions inside a fixed block of white cells.