Conway's Game of Life - Introduction
	The "Game of Life" is a game with no player created by John Conway in 1970.
	The game is essentially a set of rules that applies to certain number of "cells" in a grid.
								In a grid of any dimension, each square is called a "cell"
								The 8 squares surrounding it are called "neighbors"
								Each cell can have one state: dead or live
										a cell					Usually when a cell is live, it's also
										its neighbors					said to be "populated" i.e inhabited.
										a live cell					The total number of live cells is also
										a dead cell					called population.
										population = 8
Rules
	Death			A live cell with less than 2 live neighbors dies of loneliness
				A live cell with more than 3 live neighbors dies of overpopulation
	Birth			A dead cell with exactly 3 live neighbors comes alive
	None			A cell with 2 neighbors remains in the same state
Compute			I rendered this in MS Excel using a matrix for each grid, 0 representing a dead cell
			and 1 representing a live cell. They were colored using conditional formatting.
			(every cell with value "1" is colored black)
Steps			State of the cells is updated after each step. I call the initial grid step 1, so that
			the final number of steps can't be smaller than 2, since 0 and 1 will be colored by
			the formatting rule.
End			The game "ends" when the popularity of cells equal zero (death), or reaches a
			configuration that stays the same every step (stable config), or reaches multiple
			configurations that cycle after every number of steps (oscillation). Oscillations that
			can "move" accross the plane are called spaceships.
			Apparently this definition only works with smaller grid (< 6x6) because with
			larger grids the "ending" could be a combination of deaths, stable configs,
			oscillations and spaceships. That is, if the game ever end at all.
Example			Example of a game. Each game is displayed in a row like this.
	0	0	1	1				0	0	1	1				0	1	0	1				0	0	0	0				0	0	0	0				0	0	0	0
	0	0	1	0		--->		0	1	1	1		--->		0	1	0	1		--->		1	1	0	0		--->		0	1	0	0		--->		0	0	0	0		number of steps: 5
	0	1	0	0				0	1	0	0				0	1	0	0				0	0	1	0				0	1	0	0				0	0	0	0		end: death
	1	0	0	0				0	0	0	0				0	0	0	0				0	0	0	0				0	0	0	0				0	0	0	0
		step 1							step 2							step 3							step 4						step 5 (end)							one extra step
																																				to classify the end
	The last extra step is not counted into number of steps, but it's to tell the computer each
	ending this game should be classified in.
	0	0	0	1				0	0	1	0				0	1	1	0				0	1	1	0
	0	1	1	0		--->		0	1	1	0		--->		1	0	0	1		--->		1	0	0	1		number of steps: 3
	0	1	0	0				1	1	1	0				1	0	1	0				1	0	1	0		end: stable config
	1	0	0	0				0	0	0	0				0	1	0	0				0	1	0	0
		step 1							step 2						step 3 (end)							final extra step
	In this example, the final step tells that the game ended in a stable configuration.
	0	0	1	1				0	0	1	1				0	0	1	1				0	0	1	1				0	0	1	1
	0	0	1	0		--->		0	0	1	1		--->		0	0	0	1		--->		0	0	1	1		--->		0	0	0	1		number of steps: 4
	1	1	0	0				1	1	0	0				1	0	0	0				1	1	0	0				1	0	0	0		end: oscillation
	1	0	0	0				1	1	0	0				1	1	0	0				1	1	0	0				1	1	0	0
		step 1							step 2							step 3						step 4 (end)							final extra step
	In this example, the final step tells that the game ended in an oscillation.
	Like meta stuff? Check this out.
Formula			Probably not the best ones, but this is how I do it.
					Update cell state:						example cell B8, cell + neighbors = (A7:C9)
	A7	A8	A9		=IF(B8=0,IF(SUM(A7:C9)=3,1,0),IF(SUM(A7:C9)<5,IF(SUM(A7:C9)>2,1,0),0))
	B7	B8	B9		if cell is dead --> if there's 3 cells around --> live, otherwise dead.
	C7	C8	C9		if cell is live --> if there's less than 4 cells around --> if there's more than 2
					cells around --> live, otherwise dead.
/	A1	A2	A3	A4	A5	A6	A7	A8	A9	A10	A11	A12	A13	A14	A15		Calculate steps:
A1	1					2					3						=A$6
B1
C1	0	0	0	1		0	0	0	0		0	0	0	0			Calculate end:
D1	0	0	1	0		0	0	1	0		0	0	0	0			=IF(SUM(A11:F14)=0,"death",IF(AND(EXACT(A11:F14,A6:F9)),"stable config","oscillation"))
E1	0	1	0	0		0	1	0	0		0	0	0	0			if final population = 0 ---> death, if not:
F1	1	0	0	0		0	0	0	0		0	0	0	0			if the two last matrices equals each other exactly ---> stable config, otherwise oscillation.
	Calculate stats:					(provided that the games starts at line 8)
	deaths					=COUNTIF(8:1048576,"death")
	oscillations					=COUNTIF(8:1048576,"oscillation")
	stable configs					=COUNTIF(8:1048576,"stable config")
	total number of steps								=SUMIF(8:1048576,">1")
	total number of games								=COUNTIF(8:1048576,"steps:")
	average number of steps								= total steps / total games
	END.