Download 2DCA - Malcolm Pollack

Using the 2-D CA Program:
Rule types are as follows:
Nine-cell totalistic: the new state of the cell is determined by the total number of black cells in the
active cell’s vicinity (its eight neighbors and the active cell itself). 1024 possible rules.
Eight-cell totalistic: same as the nine-cell rule, except that the active cell itself is not included in the
total. 512 rules.
Five-cell totalistic: same idea as the rules above, but only the active cell itself, and its immediate
neighbors in the four cardinal directions are summed. 64 possible rules.
Four-cell totalistic: same as the five-cell rule, except that the active cell itself is not included in the
total. 32 rules.
Four-cell elementary: The active cell’s new value is determined by the position and state of its four
orthogonal neighbors. Elementary rules, unlike totalistic rules, can lead to asymmetric behavior. 65,536
possible rules (at present I am not entirely sure that my numbering system for these rules is the same as
Wolfram’s, which is expressed in terms of a Mathematica sorting formula).
“Game of Life”: This is the well-known eight-cell outer-totalistic rule introduced by John Horton
Conway. Outer-totalistic rules are a sort of hybrid between elementary rules (in which the active cell’s
new state is determined by the position as well of the state of neighboring cells), and totalistic rules (in
which the active cell’s new state is determined only by the sum of neighboring black cells). Outertotalistic rules take into account the total of black cells in the vicinity, but also depend on the particular
state of the active cell. There are 218 possible rules of this type; it can also be loaded in this program as
eight-cell outer-totalistic rule 6152.
Four-cell outer-totalistic: This rule sums the active cell’s black neighbors to the north, south, east, and
west. The result also depends on the active cell’s state. 1024 rules.
Five-cell outer-totalistic: An outer-totalistic rule that examines the active cell and its four orthogonal
neighbors. 1024 rules.
Eight-cell outer-totalistic: Sums the active cell’s eight neighbors, and takes into account, like all outertotalistic rules, the active cell’s state. 262144 rules.
Nine-cell outer-totalistic: Sums the active cell’s eight neighbors, and the active cell itself. 262144
rules.
To specify a rule number, enter it in the Rule text box.
To begin, select a rule type and a rule number, then an initial condition, then click Load. You can also,
at any time, add lines or pixels directly to the screen with the mouse, by right-clicking and dragging.
Available initial-condition selections are described below:
Random fills the screen with randomly chosen black pixels. The %Black parameter varies the
percentage of pixels that will be chosen to be black.
Chessboard fills the screen with alternating black and white pixels.
One cell, center, as you might imagine, places one cell in the center.
10 x 10 random places a 10 x 10 block of randomly valued pixels in the center of the screen. As above,
the %Black value determines the percentage of black pixels.
10 x 10 chessboard places a 10 x 10 pattern of alternating black and white pixels in the center of the
screen.
Horizontal line draws a horizontal line at the vertical center of the screen, with random black pixels. To
draw a solid line, set %Black to 100.
Vertical line draws a vertical line at the horizontal center of the screen, with random black pixels. To
draw a solid line, set %Black to 100.
Diagonal line draws a line descending at 45° from the upper-left corner of the screen, with random
black pixels. To draw a solid line, set %Black to 100.
Cross combines the Horizontal line and Vertical line initial conditions.
Diagonal cross draws lines descending at 45° from the upper corners, with random black pixels.
The Checked starting conditions draw lines and crosses made up of alternating black and white pixels.
The Block and Square conditions draw the indicated pattern in the center of the screen.
To change the dimensions of the screen, use the “Width” and “Height” buttons, then click “Set”.
While running a CA you can single-step the rule’s evolution by clicking “Stop”, followed by “Next”.
The CAs are wrapped toroidally – the top connects to the bottom, and the sides wrap around.