This is a site about Cellular Automata(the plural form of Cellular Automaton), used in a recreational manner. That is, purely for the aesthetics of their output, rather than any capabilities to model physical or theoretical systems. Cellular Automata are based on the computer science concept of Automata Theory. A very basic explanation of automata theory is that it seeks to describe systems in terms of all the states they can exist in, and how each input changes those states and outputs, or Finite State Machines. As an example, consider a soda vending machine. As you enter quarters, its state changes. In order to change it to the state which results in the output firing to dispense a soda, you need to enter the correct number of quarters. You may also press the coin return, which resets the state and returns the quarters which have been deposited since the last purchase. See the example of a Finite State Machine describing the operation of a soda vending machine, below. Assume the cost of a soda is 50¢

In the above system, there are 5 states. They are: start, 25¢, 50¢, dispense soda, and return coins. Different inputs causes the machine to transition from one state to another. For example, if in the start state, an input of 25¢ to the machine will cause it to enter the 25¢ state. Each line represents an input, which causes the state to change. The example is simplified to convey the idea.

A Cellular Automaton is much like finite state machine, but different in that it consists of many machines called cells, which exist within a neighborhood of other cells. The states of these neighboring cells will be the sole determining factor of the state of the cell in question. In the 1 dimensional automata that I have used to generate the black and white art based on Wolfram Notation, there are only two states, black and white. However, there are two neighbors, which including the cell itself, makes 3 states to track. So, if each machine can be in one of two states, and there are 3 machines, this means there can be a possible 2³, or 8 transformations. I have illustrated the possible transformations below. Since each outcome can have one of 2 states, and there are 8 possible outcomes, the total number of different rules in this system is 2⁸ or 256 rules.

Each individual number represents one set of possible predecessor states, and the outcome, on the line below. This automaton is based discrete time steps. This means that there are finite, discrete steps in time during which actions occur. Each cell observes the state of its neighbors and its own state, then decides to change its state, depending upon the current rule governing transitions. All the cells update their state at the same time. Since this is a theory object, we can assume that all these actions can actually take place, perfectly aligned in time. In reality we know that simultaneity is only an illusion which can be dispelled by finer measurements of time.

In this example, all outcomes are the state "white." So, no matter which cells were black in the initial configuration of the automaton, the very next time step would see all the cells turn white. This rule, depending upon whether you count 1 as white or black, would be either 00000000(in binary) or 0(in decimal), and 11111111(in binary) or 255(in decimal). The idea is to translate the numbers between(and including) 0 and 255, and turn them into rule descriptions, with their 8 different bits describing the output of a specific transformation.

I have written a program which I use to generate and display these states. A single row of active cells is used to generate one row of pixels at a time, which "grow" out of the active cell like a fingernail, one row of cells at a time. There are controls which allow the operator to change the rule as the program is running. This is where one may observe abrupt changes in style or color. Often horizontal lines will be implied by the differing styles.

The above is an example of such an image. Notice that the program begins with a single black cell in the middle, and grows upwards, pushing the older rows towards the bottom, so that the newest row is at the very top of the image.