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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