Recent discoveries in Conway’s Life

This is breaking news, by the way; hence, the article is somewhat rushed. (If you haven’t heard of Conway’s Game of Life, there is a summary on Wikipedia.)

As of a few minutes ago, Mike Playle discovered a π/2 stable reflector with a recovery time of 43 generations, which is an order of magnitude faster than its competitors. Here it is in the form of the first period-43 oscillator; it can be trivially modified to yield any period ≥ 43 (including 53, which hadn’t been attained until now).


Due to the small size of 19 × 23 pixels, he wins a prize of $100 from Dave Greene, which had remained unclaimed for twelve years! Similarly, the fast recovery time of 43 generations earns an additional $100 from Matthias Merzenich. It appears that Ed Pegg’s prize puzzle page needs updating to reflect (no pun intended!) this discovery.

Coincidentally, the beta of Golly 2.5 has also just been released.

Slightly older news

Also recent, but not quite as recent, was Josh Ball’s discovery of a tiny c/7 spaceship. There are now nine orthogonal spaceship velocities, summarised in this infographic I prepared earlier (note the Ford circles):

Dave Greene, Hartmut Holzwart and I are currently involved in the process of engineering a 31c/240 spaceship, so that might be appearing reasonably soon. It is likely to be rather large, though.

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10 Responses to Recent discoveries in Conway’s Life

  1. wojowu says:

    “Rather large”, huh? Is it going to be comparable to Caterpillar, or maybe more reasonable size?

    • apgoucher says:

      Comparable to the Caterpillar, but maybe slightly smaller due to the lack of helix.

    • paul wilson says:

      The Caterpillar is too vast for my laptop AND any graph paper I have, and I also have serious problems with spacing & accuracy in very huge patterns. I’ve made mistakes that caused me to question my sanity and/or mental abilities. Ever since 1970 I’ve been playting LIFE and I am now trying to just sit back and rest on my laurels.

      As for the Caterpillar, which looks like the Freedom Tower and is similar in size (10 units/inch scale), I’ve contented myself with the core reaction, a collision bet the Pi-Heptonimo and a blinker.

  2. Ed Pegg Jr says:

    Very neat. I’ll update my prize page

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  4. Pingback: Implications of the Period 43 stable reflector | Question and Answer

  5. paul wilson says:

    I notice that C/2 spaceships are often made of “snap-on” parts and I’ve engineered some that way, whereas lower speeds like 2C/5 C/5 C/6 and the unique C/7 do not lend themselves to that phenomenum. Also extensions of C/2, C/3 are easy to build, but the lower speeds – nada.

  6. paul wilson says:

    I’ve graphed a P256 oscillator, using 4 eaters to suppress the gliders from a P256 Herschel Gun. I had to run the pattern while building it, to get the herschel and the blocks properly positioned each P64 subperiod. I also had to keep checking the graph, to see if my spacing hadn’t gone awry. I make my own graph paper on computer now, since my supply store shut down on me.

    With a proposed P598 oscillator, spacing ,timing, and graph paper problems discouraged me from even cataloging the engine. Where 2 gliders interact with 4 P46 twin bee oscillators to change into 2 LW spaceships, collide headon, become 2 gliders again. make their way to the oscillators and become LW spaceships in collision course again.

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  8. Pingback: Implications of the Period 43 stable reflector - MathHub

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