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« Update: smaller Garden of Eden previously known | Main | Frozen LWSS fuse / rake »

2007 December 15

Engineered Objects
Prime Number Calculators

Four prime-number calculators:
-- 1st quadrant (upper right):
Original sieve by Dean Hickerson, 1 November 1991
-- 2nd quadrant (upper left): new sieve #1
Uses every glider relay, p60 instead of p40 LWSS rake.
-- 3rd quadrant (lower left): new sieve #2
Vertical guns replaced with an equivalent reflector.
-- 4th quadrant (lower right): new sieve #3
Contains no glider guns, only pentadecathlon reflectors.

New sieves by Jason Summers, 15 October 2005.
A few years ago Jason Summers constructed three new versions of Dean Hickerson's 1991 Life prime-number calculator. These all produce the same strings of spaceships: an LWSS appears at time 60N if and only if N is prime. This is twice as fast as the original 1991 pattern, which is included for comparison (upper right quadrant).

In the pattern at right, the LWSS streams from the two bottom quadrants are set up to annihilate each other. The top two streams -- one at 60N and one at 120N -- are reflected upward along the central axis for comparison purposes. The spaceships representing 2, the first number in each series, are exactly in alignment.

Detail of four-primers pattern
Detail of four-primers pattern after 100,000 ticks.
All four quadrants use the same basic structure of reflected gliders to perform the prime-sieving operation. After running 100,000 generations in Golly (which seems fairly quick, in spite of the lack of regularity in the northbound output) the center of the above pattern looks like this:

Posted by Dave Greene on 2007 December 15 09:35 |