Making names in Life

The Game of Life is a cellular automaton invented by John Conway in 1970, and popularised by Martin Gardner.
In Life, cells on a square grid are either alive or dead. It begins at generation 0 with some cells alive and some dead. The cells' aliveness in the following generations are defined by the following rules:
Starting positions can be found which lead to all kinds of behaviour: from making gliders to generating prime numbers. The following starting position is one of my favourites:
It looks boring enough, but in the next generation, it will look like this:
If you want to confirm that I'm not lying, I recommend the free Game of Life Software Golly.

Going backwards

You may be wondering how I designed the starting pattern above. A first, it looks like a difficult task: each cell can be dead or alive, so I need to check every possible combination until I find one. The number of combinations will be \(2^\text{number of cells}\). This will be a very large number.
There are simplifications that can be made, however. Each of the letters above (ignoring the gs) is in a 3×3 block, surrounded by dead cells. Only the cells in the 5×5 block around this can affect the letter. These 5×5 blocks do no overlap, so can be calculated seperately. I doesn't take too long to try all the possibilities for these 5×5 blocks. The gs were then made by starting with an o and trying adding cells below.

Can I make my name?

Yes, you can make your name.
I continued the search and found a 5×5 block for each letter. Simply Enter your name in the box below and these will be combined to make a pattern leading to your name!
Enter your name:

Similar posts

Visualising MENACE's learning
Building MENACEs for other games
MENACE at Manchester Science Festival
The Mathematical Games of Martin Gardner


Comments in green were written by me. Comments in blue were not written by me.
 Add a Comment 

I will only use your email address to reply to your comment (if a reply is needed).

Allowed HTML tags: <br> <a> <small> <b> <i> <s> <sup> <sub> <u> <spoiler> <ul> <ol> <li>
To prove you are not a spam bot, please type "sixa-y" backwards in the box below (case sensitive):


Show me a random blog post

Jan 2021

Christmas (2020) is over
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼
▼ show ▼


european cup manchester science festival binary arithmetic menace the aperiodical programming phd tennis convergence oeis twitter ternary captain scarlet weather station news estimation interpolation advent calendar london pi approximation day polynomials dragon curves gaussian elimination sound logic a gamut of games fractals approximation football preconditioning dataset squares error bars bempp martin gardner pi puzzles big internet math-off national lottery matrix multiplication chalkdust magazine simultaneous equations rhombicuboctahedron signorini conditions sobolev spaces chess mathslogicbot electromagnetic field accuracy inline code raspberry pi pac-man golden ratio matrix of minors bodmas wool logs speed python christmas bubble bobble go realhats computational complexity chebyshev latex misleading statistics nine men's morris flexagons php propositional calculus manchester quadrilaterals hannah fry boundary element methods draughts graph theory inverse matrices talking maths in public hexapawn cross stitch asteroids folding paper dates weak imposition harriss spiral trigonometry mathsjam reddit radio 4 game of life geometry frobel finite element method data visualisation ucl probability machine learning matrix of cofactors golden spiral books world cup gerry anderson royal institution pizza cutting braiding light mathsteroids palindromes statistics final fantasy stickers matt parker people maths graphs hats coins reuleaux polygons tmip plastic ratio folding tube maps games rugby countdown wave scattering map projections sorting triangles determinants london underground matrices platonic solids christmas card curvature sport cambridge data royal baby video games exponential growth javascript noughts and crosses numerical analysis pythagoras game show probability craft geogebra


Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2021