John Conway's 'Game of Life'.

I have been silent for a week or two, locked down by covid-19, and getting two e-books ready for release, one of these, Playwiths, is STEAM activities suitable for young minds, retired engineers and parents looking for stuff to enlighten minds.

A goodly part of that is recreational mathematics, so when I heard this morning that John Conway had fallen victim to the nasty virus, I felt ashamed that I had never written anything about his delightful Game of Life.

That involves higher mathematics and I mainly do lower mathematics, so this is just to get you started.

John Conway’s Game of Life

In October 1970, fans of recreational mathematics encountered The Game of Life in Scientific American. In those days, before personal computing, we either had programmable calculators or we used pen and paper to amuse ourselves. The calculators couldn’t do Life for us, so it was done on paper. A few, a very few, were able to play it on university computers, but I was a paper player.

All you needed was a grid with some coloured in squares, and a set of rules for generating a new set. A cell that was filled in was live, one that was empty was dead. In the next generation:

any live cell with fewer than two live neighbours died;
any live cell with two or three live neighbours lived on;
any live cell with more than three live neighbours died;
any dead cell with exactly three live neighbours became live.

The simplest starters or seeds were called Still Lifes, because they never altered

 Four still life forms: block, beehive, loaf and tub

Some seeds alternated between two types, and these were called Oscillators. To find out why they get their name, you will need to take up pencil and paper, or look up <“game of life” oscillators> Here are some oscillator seeds, named blinker, toad and beacon:

From left to right, blinker, toad and beacon.

To see how you analyse these shapes, here are marked-up versions of the two stages of the beacon:

  Beacon stage 1        and        Beacon stage 2

This is one to research for yourself, because there isn’t room for any more here, except to note that this shape, known as the r-pentomino, is a methuselah.

The r-pentomino.

And the other e-book? It's called Looking at Small Things, and it's about wee beasties, small bits on plants and animals and other fine detail, using all member of lenses and microscopes. I'm still tidying up around the edges for Small Things, but if you look in the links, you can see how to buy the book from Amazon Kindle, or get it for free.