PascGalois Zn Help: 2-D Cellular Automata Setup Screen


The setup screen for 2-D Automata is pictured below.

The screen is broken into three sections, options, seed and update rule.

The Options Section

The options section consists of just a couple settings that are needed to define an automaton. When graphing an infinite automaton you will have only one option to set, the default element, but when you are graphing a finite automaton you will also see options for wrapping, the size of the grid and the seed placement.

The Seed Section

Setting the seed for a 2-D automaton is very similar to setting the seed for a 1-D automaton. The only difference is that each level consists of a grid of values. The Seed tab looks like,

Each level of the seed represents a time-step of the automaton. If your update rule goes back only one time-step then you will need only one level in your seed. If you use more than one previous time-step in the update you may want to have more than one seed level. Recall that if the update rule must go outside the automaton (including the seed) it will use the default element.

You can set the number of rows, columns and levels by the spinners above the grid. Also the Viewing Level spinner tells you what level you are currently looking at. The program can take a maximum of 100 rows, 100 columns and 20 levels. Once the number of rows, columns and levels are selected simply fill in the grid with the seed elements you wish to use.

The Seed Toolbar

There are five tools for the seed tab.

The Update Rule Section

Setting the update rule for 2-D automata is similar to that for the 1-D automata. As with the seed the only difference is that you are working with levels of grids instead of rows. The Update Rule tab looks like,

The rule is any valid group theoretic expression that uses variable names for the group elements and integers for the exponents or coefficients. Juxtaposition is not recognized, you must use a * to denote multiplication. Powers are denoted by ^ and any negative powers must be put in parentheses. Variable names can be any string of letters. Numbers, underscores and special characters are not permitted. For example, the following are legitimate update rule expressions, a*b, a^2+b, b+a*b^(-1), a*b*a^(-1)*b^(-1), and a^3+b^(-4). The following are not legitimate expressions, a^2b and a*b*a^-1*b^-1.

The update grid is how you tell the program where to get the elements that are to be used in the update formula. There must be one and only one X in the entire grid and it must be on the last level of the grid, but it may be in any position on that level. The position of the X tells the program that this is the cell to be updated. The other entries are names of variables used in the update rule. When the program generates its data it will start at the X and substitute the respective cell entries in for the corresponding variables in the formula to determine the value of the new cell.

The Update Rule Toolbar

There are five tools for the update rule tab.


Related Links: