![]() With zero (white-white-white) being the lowest and six (black-black-black) the highest sum, a rule will have to assign a next state to seven initial states. Then the combination black-green-green has a total value of 2 + 1 + 1, or four and is in that sense identical to black-white-black, which also sums to 2 + 0 + 2, or four. Say white, green and black correspond to zero, one and two. ![]() That means the next value depends on the total of the values of the cell and its neighbours. ![]() The automaton I'm making is a so-called totalistic automaton. Each possible configuration of a cell and its neighbours is mapped onto another value. Below is an illustration of a rule, which we'll come to know as rule 136. The rule simply maps each of those states onto a resulting value for the cell. If a cell has one of three possible values, the combination of a cell with its left and right neighbours can be in 3 3 or 27 states. In most cases, a cell changes state depending on its own value and the value of its immediate neighbours. This system reveals triangular patterns over the first 150 generations. Each horizontal line represents an iteration or a generation. The system starts at the top with a single green cell. Example of a one-dimensional automaton with three states: white, green, or black. Each iteration of the system corresponds to a row of cells, and we can stack the rows to visualise the evolution over time. I wanted to create a simulation of a different automaton one with a single dimension, but with cells that can be in three states. The universe of the Game of Life is a two-dimensional grid with cells that can be in two states: zero or one, dead or alive, white or black. The best known example is the Game of Life. ![]() By applying a transformation rule over and over, these visuals often reveal intricate patterns, ranging from repetitive mosaics to seemingly organic structures. Visualisations of automata typically use colours to represent the different values or states of a cell. This is a gentle exploration of cellular automata.Ī cellular automaton is a system of cells in a grid, each containing a numerical value that changes over time according to a rule. ![]()
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January 2023
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