Update: It seems I got all this wrong (again!). See Hugh’s comment here
A little while ago I wrote of how I had challenged the children I work with in a Code Club to find the glider pattern in Conway’s Game of Life.
I suggested that, if they adopted an essentially random approach to putting down counters within one cell of existing counters they would need about three weeks of continuous work to find the solution as there are about 30,000 such patterns and I estimated it would take a minute, on average, to check the solution for longevity. (In fact I over estimated the average time by 50%, because, of course we should expect to trip over the correct solution, on average, at the half way point – if we adopted a truly random approach to this of course.)
Hugh who is a regular and learned commentator here then drew my attention to sequence A094169 in the “Online Encyclopedia of Integer Sequences” to suggest that there were only, in fact 3,230 possible solutions to be checked – as that is the number of five cell polyominoes (to be fair to Hugh he suggested that polyominoes were not the only potential solutions of interest).
In fact if we looked at polyominoes we would never find the solution – as the glider is not a polyomino – none of the five configurations has every counter/cell joined edge to edge.
But I am again forced to reduce the time – because there are essentially five glider patterns (or if you like any one glider pattern is isomorphic to four others) – and any one of them would do – so we are left with an expectation that we’d find the pattern in about 3,000 random tests – more or less the same number as the count for the pentominoes.
- Why IT Monotony When Smarter Computing is Available? (smartercomputingblog.com)
- Recent discoveries in Conway’s Life (cp4space.wordpress.com)
- Integers and Sequences Solution (tanyakhovanova.com)
- Conway’s Game of Life Watch (makezine.com)
- Game of life – dlow ticker (dltw.wordpress.com)
- A suffix prime (johndcook.com)
- Conway’s Game of Life in Processing.js (davidshimel.com)
- Amy’s Game of Life (raspberrypi.org)