Elementary rule 73:

Generate the same result using RulePlot:

3-color rule 679458:

Generate a rule icon:

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 f 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; #2 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:

Specify rule 30 using an association:

3-color cellular automaton:

2-color range-3/2 cellular automaton:

3-color totalistic cellular automaton:

3-color outer totalistic cellular automaton:

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 the space-time history as a 3D image:

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:

Use RulePlot to visualize the totalistic rule specification:

5-neighbor totalistic rule:

5-neighbor outer totalistic rule:

Use RulePlot to visualize the outer totalistic rule specification:

Use an initial condition with two black cells, specified in a sparse array:

3D nearest-neighbor totalistic cellular automaton:

Specify 2D totalistic code 14 using an association (with a 9-cell neighborhood assumed):

5-neighbor totalistic code 26:

Describe the neighborhood using the string "VonNeumann":

5-neighbor outer totalistic code 110:

Growth rule in which cells get value 1 when they have 1 or 2 neighbors (of 9) with value 1:

3D image:

Growth-decay rule in which cells get value 1 when they have 1 or 2 neighbors with value 1, and get value 0 if they have 6 or 7 neighbors with value 1:

Rule in which cells get value 1 when they have 1 or 2 neighbors with value 1, keep their value if they have 6 or 7 neighbors with value 1, and get value 0 otherwise:

Rule in which cells get value 1 when they have 1 neighbor (of 7) with value 1:

Rule in which cells get value 1 when they have 1 neighbor (of 27) with value 1:

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:

Specify the rule in operator form:

Rule 30 specified as a string:

The Game of Life rule specified using a string: