# Blog

## Archive

Show me a random blog post**2019**

### Jun 2019

Proving a conjecture### Apr 2019

Harriss and other spirals### Mar 2019

realhats### Jan 2019

Christmas (2018) is over**2018**

**2017**

**2016**

**2015**

**2014**

**2013**

**2012**

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**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:

- Any live cell with four or more live neighbours dies of overcrowding.
- Any live cell with one or fewer live neighbours dies of loneliness.
- Any dead cell with exactly three live neighbours comes to life.

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

*g*s) 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*g*s 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!

### Similar posts

Building MENACEs for other games | MENACE at Manchester Science Festival | The Mathematical Games of Martin Gardner | MENACE |

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