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HomeUncategorizedConway's Game of Life: Mathematics and Construction

Conway’s Game of Life: Mathematics and Construction

This book provides an introduction to Conway’s Game of Life, the interesting mathematics behind it, and the methods used to construct many of its most interesting patterns. Lots of small “building block”-style patterns (especially in the first four or so chapters of this book) were found via brute-force or other computer searches, and the book does not go into the details of how these searches were implemented. However, from that point on it tries to guide the reader through the thought processes and ideas that are needed to combine those patterns into more interesting composite ones.

While the book largely follows the history of the Game of Life, that is not its primary purpose. Rather, it is a by-product of the fact that most recently discovered patterns build upon patterns and techniques that were developed earlier. The goal of this book is to demystify the Game of Life by breaking down the complex patterns that have been developed in it into bite-size chunks that can be understood individually.

Whether you are using it for self-study or a course, the textbook can be downloaded as a PDF file free of charge. We recommend that you view the PDF in a stand-alone PDF reader like Adobe Acrobat (which is also free), not your in-browser PDF viewer, so that you can click on pattern images to view their RLE encodings (which you can then copy and paste into Life software like Golly).


Book in PDF Format (Free, 91.23 Mb)

If you like the book then donations are appreciated, but by no means required:


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A hardcover color-printed physical version of the book is available for purchase all around the world. The printed version of the book contains the exact same content as the free PDF above. However, there are minor layout changes (e.g., no watermark, different margins) that make it look better when printed.


Buy from Lulu.com

Some photos of the book are provided below.

The hardcover book is also available at other bookstores like Amazon, Barnes & Noble, and AbeBooks. We have ordered test copies from a few different retailers, and Lulu’s print quality seems to be the best (but we cannot make any actual guarantees about print quality, as we are not involved in that process). Our Amazon and Barnes & Noble test copies were each about a half-inch thinner than Lulu’s copies, because they were printed on much thinner paper and often the reverse sides of the pages could be seen through the empty parts of the figures.

Full disclosure: we also receive a higher royalty from Lulu than from any other retailers.

If you would like a signed bookplate or a copy of the book signed by both authors, contact us at book@conwaylife.com for pricing and/or information.

Typos and mistakes in the book are collected here, as are major discoveries that were made after the book was finalized on January 15, 2022. Additional typos and anachronisms can be added directly to that page, or can be sent via e-mail to book@conwaylife.com.

  • Authors: Nathaniel Johnston and Dave Greene
  • Publisher: Self-published
  • Publication year: 2022
  • DOI: 10.5281/zenodo.6097284
  • ISBN: 978-1-794-81696-1
  • Pages: 492
  • Dimensions: US letter (8.5 × 11 in)
  • Physical book: Hardcover, color printing, roughly the size and weight of a ream of US letter paper

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