Game of Life News

Nicolay Beluchenko has found a host of new ^c/₄ Diagonal Spaceships. The smallest has only a population of 40 bits. Many of these are related by being made up of simpler subparts, having extensible sections, or by adding tagalongs to previously known spaceships. Except for the sample shown at right, these are all presented in no particular order.

# posted by H Koenig @ 16:29

Jason Summers has found configuration of stable objects (shown right) which can restore themselves when hit by a pair of sparks. The reaction takes 20 generations to stabilize, and the sparks are easily accessible, so this can be used in a number of period doubling reactions.

The top row of oscillators to the right show how the reaction can be used to triple oscillators with periods of 7, 8 and 9 to create oscillators with periods of 21, 24 and 27. The second row shows doubling reactions with periods 15, 16 and 18 going to 30, 32 and 36 respectively. It should be possible to double any period between 10 to 19.

Finally, the reactions can be chained together to create a Period 22 wick.

Update: 2005-08-20

Jason Summers has also found some new Period 72 Oscillators based on a pair of B-Heptominos pseudo-shuttle. The examples show how a single pair and two pairs can be supported by smaller period oscillators.

# posted by H Koenig @ 15:56

Around the end of July, Nicolay Beluchenko and Hartmut Holzwart produced a series of "anteater" spaceship patterns which could provide a moving c/4 diagonal termination point for an oblique wave of "ants". "Ants" wicks are unusually versatile, in that each eight-bit "ant" can follow directly behind the previous ant, or it can be offset by either one or two cells.

In the patterns that follow, each ant must be offset one cell from the previous one. With this configuration, each individual ant is a P1 pattern that travels due south at the speed of light, but the wave of ants as a whole can also be interpreted as a P4 pattern traveling northwest at c/4, thus matching the speed and direction of the c/4 terminal pattern.

The waves of ants should be assumed to extend to infinity (so don't run these spaceships for too many ticks -- they tend to crash when they run out of ants.) The construction of a matching antstretcher for these anteaters is currently an open problem.

Left: c/4 diagonal anteater: Nicolay Beluchenko, 29 July 2005
Right: c/4 double anteater

Left: c/4 anteater-related spaceships
Right: anteater-related double puffer based on Hartmut Holzwart's 29-bit spaceship (B29)

Left: c/4 anteater connected to puffer: Nicolay Beluchenko, 29 July 2005
Right: central glide-symmetric anteater element used as a tagalong: Nicolay Beluchenko, 30 July 2005

Left: alternate anteaters connected to sparking ships using glide-reflecting tagalong elements: Nicolay Beluchenko, 30 July 2005
Right: small anteater based on c/4 domino-spark ship: Hartmut Holzwart, 4 August 2005

# posted by Dave Greene @ 12:46

David Bell has constructed two new smaller sawtooth patterns. The first one undercut the size of the previous smallest known sawtooth by 6 cells.

To improve on this new record, Bell constructed a 4-engine Cordership with a minimum population of 134, compared with the 3-engine Cordership's minimum population of 149:

There is at least one other variant with a larger population, but which still beats the 3-engine Cordership. This has a minimum population of 136:

The problem with the 3-engine Cordership is that the 2-engine "wing" component swings wildly in population from small to large, and in the 3-engine Cordership the two (overlapping) wing components are locked together in a non-optimal relative phase, so that whenever one half has a small population, the other half has a large population.

By adding another switch engine in the middle to create two independent wing components, the relative phases can be adjusted in an optimal manner to reduce the population, even taking the extra switch engine into account.

Note: these new Corderships have a smaller minimum population, but the 3-engine Cordership still has a smaller average population. The average population of the 3-engine Cordership is 193.125, whereas the average population of the 134-cell-minimum Cordership is 217.854.

David Bell constructed a sawtooth with a minimum repeating population of 262 based on the 136-cell-minimum Cordership:

Bell has also created a revised moving-sawtooth pattern using the small c/3 period 27 rakes discovered since they were constructed. Further optimization is probably still possible.

The pattern works in the same way as Bell's previous moving sawtooths, by using the output of c/3 rakes to ignite the blinkers from a c/2 blinker puffer, with the number of blinkers to be consumed growing on each cycle.

Another possible sawtooth design using 'lineship' technology, which Bell has not been able to complete as yet, is presented here.

# posted by Dave Greene @ 00:40

Nicolay Beluchenko has noticed that a previously known spaceship can be converted into a small Tubstretcher. As shown at left, the four blue bits convert the ship into the smallest known puffer of any variety.

This puffer can be combined with a Tub burning fuse, found by Harmut Holzwart, to create spaceships of any length. The smallest, at 74 bits, is shown here. (The Tub fuse is hilighted in blue.)

# posted by H Koenig @ 16:35

Nicolay Beluchenko has found some new ^c/₄ diagonal spaceships. He also noticed that some previously known spaceships can be reworked and combined to yield a series of extensible ships.

Finally, he also discovered a 150 Bit Period 28 diagonal puffer which creates a Tub and a Beehive every cycle.

Update: 2005-Aug-06

A few more diagonal spaceships found by Nicolay Beluchenko.

# posted by H Koenig @ 19:21