Fundamentals: "totalistic" cellular automata

A cellular Automaton (CA) is an amount of cells, each have a defined, almost discrete state (initial state). A rule, which considers the cell state and the state of defined neighbour cells, determines the cell state of the next generation.The cells may arranged in a line (1-dimensional), in a plain (2-dimensional) or higher dimensions.
One of the most famous CA is the Game of Life by John Conway from the 1970ies. It's 2-dimensional.

But with GeZA you can explore CA only in one dimension, just one line. The second dimension will show here the temporal lapse. This means that the ongoing generations are arranged from the top to the bottom. For example here the rule 0100, resp. 01 (missing digits GeZA interprets as 0).

 

initial state (= 0. generation) is one cell with state 1 (green), all other 0 (white).

Rule 01 (3 Neighbours) means the following instruction for computing the next generation:
In this case a cell may have only the state 0 (white) or 1 (green)

sum from the 3 neighbor  cells (left, middle, right)

0

1

2

3

state of the (middle) cell  in the next generation

0

1

0

0

This rule is left/right symetric. The CAs which rules depends only on the sum of the neighbours are called "totalistic".

The digit in the nth pos give the state for the new generation, if the sum of the neighbor states is n-1. For example: sum is 3, the the state in the next generation is given by the 4th position of the rule. Doesn't this position exist, it will become 0. This  notation is different from Wolfram.
7 additional Characters geting the following special functions:

character
 function
=
 the cell keeps the state.
+
 state of the cell is incremented by 1, 9 goes to 0.
-
 state of the cell is decremented by 1, 0 stays 0
!
 0 goes to 1, otherwise the state is 0.
?
 the cell gets a random state (0..9)
>
 the cell gets the highest state from neighbours.
<
 the cell gets the lowest state from neighbours.



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