fundamentals standard

A cellular automaton consists by a lot of cells, every one have a defined, mostly discrete state (starting configuration). A rule, which considered the state of the cell itself and the states of an amount of neighbour cells determined the state in the next generation. The cells may be elements of a line (1-dimensional), a plane surface (2-dimensional) or of higher dimensions too..

One of the best known cellular automaton is the "Game of Life", discovered by John Conway in 1970. The cells are positioned on a field (2-dimensional).

GeZa-2d treats only 2-dimensional cellular automata. The cells are positioned on a grid regular.
  
The left picture shows a chessboard arrangement and is used here for mode standard, WaTor, brians brain and HPP.
The right picture shows a shifted grid and is logical the same as a honeycomb. It is the base of the mode hexagonal.
There are much more tilings thinkable. In the following description only the standard mode is treated.

The single cell on the field have a discrete state, in this app a value between 0 and 9.
Cells with these different values are displayed with different colors (0 = black, 1 = green, 2 = blue, etc.) You may change this color sheme..
Furthermore there have to be defined a neighbourhood:
      
On the left picture you see, that the cell gets 8 neighbours (green). This is known under the name Moore neighbourhood and is used by the mentioned Game of Life.
The second is called von Neumann neighbourhood. The cell itself can be part of the neighbourhood.
In this app you can define the neighbourhood freely.

At last we have to define a transformation regulation (rule), which determines the changing of the cell values by transition to the next generation.
This app is using in standard and hexagonal mode socalled "totalistical" rules. This means all values of the neighbours are added to a sum. This sum and the rule table determines the new value of the cell.

Let's do an example::

sum values of neighbors
0
1
2
3
4
5
6
7
8
9
...
new value
0
2
1
4
3
+
=
0
0
0
...

This rule writen Ón a short form : 02143+=

starting state: (0=white, 1=green, 2= blue)

neighbourhood:  

The neighbourhood of the middle green cell consisting of 2 green, 1 blue and 5 white cells. The sum of the neighbour cells (5*0 + 2*1 + 1*2) is 4. In the rule table you find for the sum of 4 the value 3. This value 3 is therefore the value of the cell in the next generartion.
In this the neighbourhood, so gets the same cell 8 white, 2 green and 2 blue neighbour cells, the sum is therefore 6. In the rule table we find for sum 6 the equals sign =, that means the objected cell will not change the value in the next generation and stays green.

In this table you see which functional characters exist except the digits.:
character
function
=
The cell keeps the value.
+
Increments the value of the cell by 1, 9 goes to zero.
-
Decrements the value of the cell by 1, 0 stays 0..
!
0 goes to 1, otherwise the value of the cell gets 0.
?
The cell gets a random value
>
The cell gets the largest value of a neighbour.
<
The cell gets the smallest value of a neighbour.


Overview