mscroggs.co.uk
mscroggs.co.uk

subscribe

Blog

Making names in Life

 2016-06-05 
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

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 "x-axis" in the box below (case sensitive):

Archive

Show me a random blog post
 2021 

Jan 2021

Christmas (2020) is over
 2020 
▼ show ▼
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

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