Mark D. Niemiec's Life Page

Format | Objects and Syntheses | Recent changes to these pages | About | Copyright

This page and its subordinate pages contain information about John Horton Conway's Game of Life.

Format of the Life pages

Object lists, and syntheses of most objects from gliders

Object sizes are determined by the number of bits in the smallest generation. Lists of still-lifes and pseudo-still-lifes up to 24 bits, period 2 oscillators and pseudo-oscillators up to 21 bits, and period 3 oscillators and pseudo-oscillators up to 20 bits have been generated or verified by computer search. Lists of higher-period oscillators and spaceships have also been generated up to 21-25 bits, compiled and extrapolated from many sources, and tabulated by hand. Lists of larger-period pseudo-oscillators and pseudo-spaceships have been extrapolated from the above.

Lists of the 19- through 24-bit still-lifes and pseudo-still-lifes are omitted for lack of space. Any application that has need of this data would find it more useful in other forms. Also, explicit syntheses have only been attempted for still-lifes up to 15 bits, pseudo-still-lifes up to 16 bits, period 2 oscillators up to 18 bits, period 2 pseudo-oscillators up to 17 bits, and other oscillators and pseudo-oscillators up to 21 bits (with some up to 25 bits). Many syntheses for larger objects also exist, but are arranged in an ad-hoc, rather than systematic fashion.

Recent changes to these pages

The history of major changes to these pages is listed on a separate page.

About these Web pages

These pages were last updated on 2015-02-19.

The information herein has been compiled by me, but is largely based on the work of many others. Attribution information is provided in general, but time and space do not currently permit individual attributions for the discovery and synthesis of each individual object. When I become aware of more information, I will try to add it to this site.

Most Life patterns here are stored in RLE format, which supports additional comment information, but the database from which these patterns are derived is currently in a different format that does not support comments. I hope to eventually convert this the database to natively use RLE format, which will make it possible to add attribution information and other comments to each of the individual patterns themselves.

I accept no responsibility for errors or omissions on these pages. While I have attempted to be as accurate as possible, errors and omissions do occasionally occur. Rely on the accuracy of the information contained herein at your own risk. Except for completeness of object lists, most of the technical information on these patterns is capable of self-verification.

Synthesis files can be verified by running them in any Life program, seeing that the "before" and "after" images end up the same, and seeing that the inputs from any steps, other than gliders and basic spaceships, are supplied by previous steps. Costs in gliders can be verified by counting the numbers of gliders and other spaceships used (with each other spaceship being weighted by the cost in gliders of creating that kind of spaceship). The appropriateness of any object in a stamp page can be verified by running the stamp page itself, and making sure the object in question has the specific population, period, and/or other properties indicated.

Of course, syntheses here only provide proof of existence of syntheses, not optimality of those syntheses. Except for those requiring 2 gliders (which have been studied to exhaustion) and those requiring 3 gliders (which are provably minimal, as they don't take 2), all other syntheses represent the best approximation of the "state of the art", and it likely that many will be subsequently improved, and many marked "unknown" will indeed have syntheses. Even those syntheses requiring 4 gliders, although most likely minimal, are not provably so; in fact, several decades after it was believed that the results of all 3-glider collisions had been explored to exhaustion, H. Koenig found a 3-glider collision to make a pentadecathlon, an object that had previously required 4 gliders.

Buckingham spent several decades doing extensive work on optimizing syntheses of all objects up to 14 bits, but even so, a few improvements to some of these syntheses have subsequently been discovered.

Comments, suggestions, corrections, and improvements are greatly appreciated, and can be sent to:


This page and subordinate pages are Copyright © 1997, 1998, 1999, 2013, 2014 by Mark D. Niemiec. All rights reserved.

Permission is hereby granted to make use of any information in these pages for non-commercial purposes.

The object lists and pattern syntheses themselves include much work by many others, and represent verifiable mathematical facts. As such, they are free of copyright restrictions.

(In other words, feel free to copy the information, but please don't create clones of the site itself without asking first.)

If you create a permanent link to this page, please send me e-mail, so I can keep you apprised of any major changes. Also, if you have a relevant page, I could add a link to it here. (Please do not create book-marks or links to sub-pages or image files, as these are liable to change without notice.)

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Copyright © 1997, 1998, 1999, 2013, 2014 by Mark. D. Niemiec. All rights reserved.
This page was last updated on 2015-02-19.