Cellular automata illustrate/model how complex structures may emerge by means of simple rules, whereas you never could detect in the rule whether they generate vast regularity, chaotic or complex forms. The automata may be simple, but also highly complex defined.

 “The cellular automaton (short CA) consists of a line of cells, each colored black or white. At every step there is then a definite rule that determines the color of a given cell from the color of that cell and its immediate left and right neighbors on the step before.” (A New Kind of Science by Stephen Wolfram, 2002 page 24) 

More complex automata are created by enlarging the neighborhood, by more dimensions or greater number of colors. Colors serve merely to visualize. Digits or symbols, any marker of distinguishable conditions could be applied.

In the simplest case a cell with one left and one right neighbor and two possible colors may have 2³ = 8 different neighborhoods. A Rule assigns to each case the color of the new cell, so there are 2 power 8 = 256 Rules.

Rule Nr.0 assigns to each case white and generates a complete white tableau, Regel Nr. 155 assigns to each case black and generates a complete black tableau. How different instead is the outcome of rule Nr.30:

From the aesthetic point of view such basic automata don’t appeal much to me. For my painting I chose a one dimensional CA with one left and right neighbor and 14 Colors. 14 Colors, because the new painting is related to my painting Nr. 131 “Gaußian Gradient” 2006. In this painting the color of each square has been determined randomly under the condition of a probability distribution, previously designed by me. For this painting I choose 14 colors, which I also apply on the new painting, but this time the color of each square is determined by the CA. So the choice of the rule was the main artistic decision.

The problem is the vast amount of rules, for the CA which I have designed has not just 256 rules you could check one by one. There are first of all 14³ = 2744 cases how 14 colors may be grouped in 3-tuples producing from that 14 power (14³) rules. A number as big as to fill a whole A4 format sheet.

The greatest possible rule would deliver a complete black array

Rule Nr. 0 a complete white one as in the simple CA. In between lies a desert to be searched and most of what I saw was monotone, I had no programm to help me here. I searched by skipping billions of rules to get a small random sample. From this I finally took the chosen rule.

Usually the representation of the automata goes line by line from top to bottom, but to observe an extended evolution of the automaton I turned it by 90°  therefore it evolves column by column from left to right.