From: (Dietrich Leithner)
Date: Thu, 18 Dec 1997 13:12:57 +0200
Subject: p57 and p56 Herschel loops

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?


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