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The first 500 powers of 3, shown in base 2. Some small-scale structure is visible, but on a larger scale the pattern seems for all practical purposes random. 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.

From Stephen Wolfram: A New Kind of Science [citation]