Elementary rule 73:
3-color rule 679458:
3-color totalistic rule with code 867:
2-color range
(two neighbors on the left and one on the right) rule 23898:
A general range
rule:
totalistic rule with code 10:
Rule 30 specified by giving explicit offsets for cells in its neighborhood:
An analog of rule 30 with modified offsets:
A rule with 2 neighbors:
Rule 30 specified by giving explicit weights for cells in its neighborhood:
A 3-color totalistic rule:
Totalistic rules have weight 1 for each offset in the neighborhood:
A 3-color outer totalistic rule:
Specify rule 90 by giving explicit replacements for neighborhoods:
Specify rule 90 by giving a single "algebraic" replacement rule:
Use an explicit Boolean formula for rule 30, operating on
True and
False states:
Values in a cellular automaton can be any symbolic expression:
Use an arbitrary symbolic function
as the rule to apply to range-1 neighbors:
Apply the function to neighbors with offsets
and
:
Set up a "Pascal's triangle cellular automaton":
Specify rule 90 as an explicit function:
Additive cellular automaton modulo 4:
The second argument to the function is the step number:
Change the rule at successive steps;
gives the step number:
Use continuous values for cells:
Specify rule 90 as a pure Boolean function:
An
analog of rule 90 specified using a pure Boolean function:
Explicit initial conditions are assumed cyclic:
The left neighbor of the leftmost cell is the rightmost cell, and vice versa:
Random initial conditions:
Start with a "seed" consisting of the block 11101 surrounded by 0s:
Start from a single 0 surrounded by 1s:
Start from 111 on a background of repeated 10 blocks:
Specify the "seed" as a sparse array:
Use a
SparseArray to give the complete cyclic initial condition:
Start from block 101 at offset
and block
at offset
:
Two steps of evolution:
Alternative form:
A list containing only the second step:
The second step, not in a list:
Steps 50 through 80:
The initial condition is step 0:
Show every third step from 0 to 100:
By default,
CellularAutomaton automatically cuts off the region not covered by the pattern:
An equivalent form:
Include all cells that could possibly be affected given the structure of the rule:
Include only the region that differs from the background:
Include all cells that could possibly be affected:
By default, different rules give regions of different widths:
Force all rules of the same type to give regions of the same width:
The region that can possibly be affected depends on the range of the rule:
Show only the region from cell 0 (the position of the initial 1) to cell 40:
Negative positions are on the left:
Give the region consisting just of cell 0 at each step:
Include only the value of cell 0, not in a list:
Show every other cell in time and space:
Cell 0 is always the leftmost cell in the explicit part of the initial condition:
Repeat a finite block to fill the region of initial conditions from positions
to
:
Evolve range-1 2D (9-neighbor) totalistic code 14 for 2 steps:
Give only the result after 2 steps:
Show the result after 30 steps:
Show the mean color of each cell:
Show a cube at the position of each 1 cell:
A spacetime slice for 50 steps across all
values at
offset 0:
Mean colors of all cells with particular
positions:
5-neighbor totalistic rule:
5-neighbor outer totalistic rule:
Use an initial condition with two black cells, specified in a sparse array:
3D nearest-neighbor totalistic cellular automaton:
Rule 30 written out explicitly as a "first-order rule":
A second-order analog of rule 30, involving two steps of initial conditions:
Include both initial-condition steps in the output:
Second-order rule 1008, starting with a single 1 in both initial condition steps:
Include both steps in the initial conditions:
Second-order totalistic rule 10 with 2 colors and range 1:
A
-order version of the same rule:
Rule 150R—the second-order reversible mod 2 rule:
A spacetime slice of a second-order totalistic rule with 2 colors and range 1:
Step 50 of the same rule:
Give the result of one step of rule 30 evolution:
An alternative form:
Iterate a single step 3 times:
Give the result of 3 steps of evolution:
Give the result as a center region surrounded by repeating background:
Rule 45 gives a background of 1s after one step:
Iterate a single step of rule 45:
, 
, elementary rule with rule number n
neighborhood 
is equivalent to CellularAutomaton
. 
. 
can contain patterns. 
, the list of neighbors is taken to be a full array with dimensions 
. 
cells to the left.
, each step depends on s preceding steps. 
, assumed cyclic 
superimposed on a b background 
superimposed on a background of repetitions of 
, 
, ... 
at offsets 
on a background 
is aligned with 
. 
generates an evolution list of length 
.
can be as follows: 
through 
, 
, ... 
uses the default Automatic for xspec. 
through 
, 
, ... 
is taken by default to have space offset 
. 
, the region that can be affected after 
steps by a cellular automaton with a rule of range 
has width 
. 
. 
. 
steps of cellular automaton evolution gives a list of length 
:
EXAMPLES
Basic Examples 
Scope 