2005-03-19

 

Pi Waves and Pi Tracks

Background

Pi Heptomino Basic Pi The Pi Heptomino, shown to the left in an alternate form which occurs in waves and tracks, is a commonly occurring pattern which in 173 generations results in a small constellation of objects. One of the earlier discoveries in the Game of Life was that a Pi Heptomino reappears 30 generations later while having moved 9 cells. This is equivalent to the Pi moving at the speed of 3c/10. Unfortunately, the exhaust immediately overwhelms the new Pi.

Basic Pi-Wave In Lifeline #3 (Sept.1971), p.18, it was reported that Denis Wilson had discovered that when an infinite string of Pis were properly spaced, the entire string moves as a wave at the speed of 3c/10. It generates a somewhat complicated exhaust which eventually disappears. No way of stabilizing the ends has been found.

Pi-Block In Lifeline #4 (Dec.1971), p.3, it was shown by Mike Beeler how a pair of Blocks allowed the Pi to reproduce several more times before being consumed by its exhaust. With two properly spaced rows of Blocks parallel to the direction of travel, the Pi can move by consuming the rows of Blocks until self-destructing when the rows end.

449P180H90V0A32.1 The rows of Blocks can be laid down by a puffer. Since no known spaceships move at the same speed as a Pi, this results in a spaceship which slowly lengthens. Here the Period 18 puffer moves at c/2, in effect every 180 generations adding 4 Block pairs to the track that will be consumed by the Pi.

Pi Crawler A single Pi can also move along a single trail of Blinkers. This Pi in the "Pi Crawler" takes 45 generations to reappear, having moved 17 cells in the process, resulting in a speed of 17c/45. As above, a puffer of another velocity can be used to lay down a track for the Pi to travel along. More importantly, a Blinker is left behind, allowing multiple Pi Crawlers to use the same trail of Blinkers. This reappearance, along with spaceships which lay down the Blinker trails, is the basis for Gabriel Nivasch's Caterpillar. See his article for more details.

Recent News

Pi Wave 2In a discussion of waves in general, Jason Summers mentioned a Pi Wave which, while not well known, was discovered a while ago, and which lays down trails of Twin Blocks. As with the clean Pi Wave, there's no known way to stabilize the ends.

New Pi WavesHe also presented some new Pi Waves in which adjacent Pis are not in exact phase with each other as with the earlier Pi Waves.

New Pi TracksAlso, Nicolay Beluchenko presented some new Pi Tracks in which a first Pi climbs the track as with the earlier Blinker trail, above. But in the process, the Pi alters the track, leaving behind a different track. A second Pi can follow on this track, cleanly burning it.

Pi HWSS trackBeluchenko also discovered a track in which a pair of streams of Heavyweight Spaceships (HWSSs) can be used to support a Pi's movements.



2005-03-11

 

New Period 7 Oscillators

P7 Jason Summers has found a way to bound a period 7 agar using the halves of a previously known period 7 billiard table oscillator (46P7).



2005-03-09

 

New Period 4 Oscillator Variants

New P4 Rotor New P4s

Scot Ellison has found a terminal element for a previously known extensible or wick oscillator. The objects in the top line were previously known, while the remaining oscillators use this new variation. The basic rotor element is also shown.



(Disclaimer— I have no association with anyone or any organization, and speak only for myself. Links and quotes are provided for information only.)