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 "tnemges" backwards in the box below (case sensitive):


Show me a random blog post

May 2021

Close encounters of the second kind

Jan 2021

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


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


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