Multiway systems can in general use any sets of rules that define replacements for blocks of elements in sequences.

The idea is to set up templates that involve complete 3×3 blocks of cells, including diagonal neighbors.

A highly compressed representation of the evolution of rule 110 from random initial conditions in which only the first cell in every 14×7 block is sampled.

The evolution of overall density for block cellular automata (c) and (d) from the previous page .

It is also easy to extend block-based encoding to two dimensions: all one need do is to assign codewords to two-dimensional rather than Examples of one-dimensional pointer-based encoding applied to patterns produced by cellular automata.

And thus for example the values of all cells represented by an integer variable a can be updated in parallel according to rule 30 by the single C statement a = a > > 1 ^ (a | a < < 1); This statement, however, will only update the specific block of cells encoded in a . Gluing together updates to a sequence of such blocks requires slightly intricate code.

[Spectra of] random block sequences Analytical forms for all but the last spectrum are: 1 , u 2 /(1 + 8u 2 ) , 1/(1 + 8 u 2 ) , u 2 , (1 - 4u 2 ) 2 /(1 - 5u 2 + 8u 4 ) , u 2 /(1 - 5u 2 + 8u 4 ) , u 2 + 1/36 DiracDelta[ ω - 1/3] , where u = Cos[ π ω ] , and ω runs from 0 to 1/2 in each plot. Given a list of blocks such as {{1, 1}, {0}} each element of Flatten[list] can be thought of as a state in a finite automaton or a Markov process (see page 1084 ).

In the limit, such sequences contain with equal frequency all possible blocks of any given length, but as shown on page 597 , they exhibit other obvious deviations from randomness. The picture below shows the k = 2 sequence chopped into length 256 blocks.

., where now the block of digits 142857 repeats forever.

Constraint 1125528937 leads to a pattern that repeats in 98×98 blocks.