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 "linear" in the box below (case sensitive):

Archive

Show me a random blog post
 2020 

Jul 2020

Happy τ+e-6 Approximation Day!

May 2020

A surprising fact about quadrilaterals
Interesting tautologies

Mar 2020

Log-scaled axes

Feb 2020

PhD thesis, chapter ∞
PhD thesis, chapter 5
PhD thesis, chapter 4
PhD thesis, chapter 3
Inverting a matrix
PhD thesis, chapter 2

Jan 2020

PhD thesis, chapter 1
Gaussian elimination
Matrix multiplication
Christmas (2019) is over
 2019 
▼ show ▼
 2018 
▼ show ▼
 2017 
▼ show ▼
 2016 
▼ show ▼
 2015 
▼ show ▼
 2014 
▼ show ▼
 2013 
▼ show ▼
 2012 
▼ show ▼

Tags

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

Archive

Show me a random blog post
▼ show ▼
© Matthew Scroggs 2012–2020