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To clean up the mistakes in your summary:

4 gliders hit each other to make a stream of gliders. This isn't a gun, because a gun costs more. instead it's a GPSE, which looks like a gun from the barrel end, but has a limit. As it approaches that limit, the RCT mechanism lets another three GPSEs generate an arbitrary list of bits, controlled by the precise location of the first (as a binary number). The final count 15 comes from the naive 4×4 minus one from being able to piggyback one of the constructions off a neighbor to save a single glider.

From bits to an embedded turing machine is gol magic that the blog post treats better than my comment could.



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