John Conway's "Game of Life"

Every empty cell with exactly three neighbors is a birth
cell.

Each cell with four or more neighbors dies from overpopulation.

Each cell with one or less neighbors dies from isolation.
Its neighborhood consists of the eight cells surrounding
a cell > all the rules will start with an '8'.
Every empty cell with exactly three neighbors is a
birth cell.
This rule is applied to any empty cell:
'V'
To have an action, there must be three cells (color 1) in
the neighborhood:
'A=3'
The action is the birth of a new cell (color 1):
'A'
The first rule is: 8VA=3A
Each cell with four or more neighbors dies from overpopulation.
This rule is applied to cells of color 1:
'A'
To have an action, there must be more than 3 cells (color
1) in the neighborhood:
'A>3'
The action is the death of the cell:
'V'
The second rule is: 8AA>3V
Each cell with one or less neighbors dies from isolation.
The third rule is: 8AA<2V
"Game of life":

8VA=3A

8AA>3V

8AA<2V
Edward Fredkin's rules

Each cell with an even number of live neighbors becomes
or remains empty

Each cell with an odd number of live neighbors becomes
or remains live
Its neighborhood consists of the four orthogonally adjacent
cells > all the rules will start with a '4'.
Each cell with an even number of live neighbors
becomes or remains empty
This rule is applied to any cell (empty or not):
'T'
To have an action, there must be an even number of neighbors:
'AM2'
The action is the death of the cell:
'V'
The first rule is: 4TAM2V
Each cell with an odd number of live neighbors becomes
or remain live
This rule is also applied to any cell:
'T'
To have an action, there must be an odd number of neighbors:
'AN2'
The action is the birth of the cell:
'A'
The second rule is: 4TAN2A
Edward Fredkin's rules:

4TAM2V

4TAN2A
These rules can easily be simplified:

4AAM2V

4VAN2A
2 colors version of John Conway's
"Game of Life"

8VN=3P

8PN<2V

8PN>3V
These rules work if you have
only 2 colors.
A third color could interact
and create mistakes in patterns
2 (or more) colors version of John
Conway's "Game of Life":

8VN=3W

8WA>1A

8WB>1B (Each mark may be used
by several rules)

8AN<2V

8BN<2V

8AN>3V

8BN>3V
Stanislaw Ulam's rules

Births occur on cells that have
only one neighbor

All live cells of generation n vanish
when generation n+2 is born
We can represent each generation
by a specific color state:

color 1 for generation n

color 2 for generation n+1
The first rule is:
4VN=1A
We now just have to change the color
state of the cell:
0A1=1B
0B1=1V
There is no condition on
the neighborhood
> 0 neighbors
> 1=1 is always true
Stanislaw Ulam's rules:

4VN=1A

0A1=1B

0B1=1V
As only cells whose neighborhood has changed during
the last turn are tested, some rules may not work:
0V1=1A wouldn't do anything on an empty map
(Try with only one cell)
 I promise to correct that on the next version 