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: