In their paper "Tight bounds on periodic cell configurations in Life" Dave Buckingham and Paul Callahan wrote (lemma 2) (Accepted to Experimental Mathematics. Electronic preprints available on request. --PBC):
"For any n >= 58, a Herschel loop can be constructed and populated with Herschels to realize a period-n oscillator."
Here are examples of Herschel loop oscillators for n = 57 and n = 56:
The loops use fast 65-step Herschel conduits that turn a Herschel left and flip it. (Also used in the above loops are fast 77-step Herschel conduits that translate and flip a Herschel. These were known before).
The 65-step Herschel conduits have the following minimum repeat times (compression):
------------------------------------ Conduit Repeat Example Period Time Application ------------------------------------ 3 57 p57 Herschel loop 4 60 p68 glider gun 8 56 p56 Herschel loop ------------------------------------The 65-step conduits also allow to shrink the size of some Herschel-based glider guns. Here is one example:
Question: Dean's stamp collection shows p56 oscillators but has no entry for p57. Is the above the first p57?
Dieter dietrich.leithner@dlr.de
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