Basic Evolution

20 steps in evolution from a blank tape.

50 steps in evolution from a blank tape.

200 steps in evolution from a blank tape.

Evolution from a sequence of initial conditions.

Head Motion

Excursions of the head over the course of 250 steps, starting from a blank tape.

Excursions of the head over the course of 1000 steps, starting from a blank tape.

Excursions of the head for a sequence of different initial conditions.

Paths for more initial conditions.

State Sequences

A representation of the states of the head for 200 steps (state 1 is an down-tick; 2 is an up-tick).

A representation of the states of the head for 500 steps (state 1 is an down-tick; 2 is an up-tick).

Transition diagram for successive rule cases used in 20 steps of evolution from a blank tape.

Transition diagram for successive rule cases used in 200 steps of evolution from a blank tape.

Cumulative fractions of different rule cases as a function of number of steps, starting from a blank tape.

Compressed Evolution

10 steps of left-compressed evolution, corresponding to 400 steps of underlying evolution.

Right-compressed evolution corresponding to 400 steps of underlying evolution.

Left-right compressed evolution corresponding to 400 steps of underlying evolution.

Direction-compressed evolution corresponding to 400 steps of underlying evolution.

200 steps of left-compressed evolution (corresponding to 129520 steps of underlying evolution).

200 steps of left-compressed evolution starting from 100 yellow cells (corresponding to 213600 steps of underlying evolution).

The spacings between successive outward jumps in 1000 steps of left-compressed evolution (corresponding to 3214932 steps of underlying evolution).

The spacings between successive outward jumps in 10000 steps of left-compressed evolution (corresponding to 323588676 steps of underlying evolution).

Causal Networks

The causal network of updating events, starting from a blank tape.

The causal network, rearranged.

The causal network from 2000 steps of evolution from a blank tape.

Function Computed by the Machine

The "function" computed on successive steps, starting from a blank tape.

The "function" from initial conditions to final states, after 10 steps.

Random Initial Conditions

Evolution with a random initial condition.

More steps with a random initial condition.