At 09:42 PM 2/14/03 -0500, you wrote: I'm wondering whether these repetitions gradually 'accrete', that is, get incorporated in larger and larger repeated subsequences. I'm also wondering whether the repetition is due to an innate tendency toward those particular subsequences, or whether there is some sort of copying process that tends to Xerox earlier subsequences under some circumstances. If the former, we would expect to see some of the same subsequences in the first differences of Ulam(1,3); if the latter, we would expect different repeated subsequences in Ulam(1,3). You see, if the content of the repeated subsequences is partly arbitrary, that is, if, in the right circumstances, anything could be copied, then we may have actual natural selection happening as the different sequences compete for space and 'attention' by the copying mechanism. I await developments. -A