Each individual node in example (b) still has exactly two connections coming out of it, but now the overall pattern of connections is such that every block of nodes is connected to four rather than two neighboring blocks, so that the network effectively forms a two-dimensional square grid.

[Excluded blocks in] dynamical systems theory Sets of sequences in which a finite collection of blocks are excluded are sometimes known as finite complement languages, or subshifts of finite type.

Huffman coding From a list p of probabilities for blocks, the list of codewords can be generated using Map[Drop[Last[#], -1] &, Sort[ Flatten[MapIndexed[Rule, FixedPoint[Replace[Sort[#], {{p0_, i0_}, {p1_, i1_}, pi___}  {{p0 + p1, {i0, i1}}, pi}] & , MapIndexed[List, p]] 〚 1, 2 〛 , {-1}]]]] -1 Given the list of codewords c , the sequence of blocks that occur in encoded data d can be uniquely reconstructed using First[{{}, d} //. … If all 2 b possible blocks of length b occur with equal probability, then the Huffman codewords will consist of blocks equivalent to the original ones. In an opposite extreme, blocks with probabilities 1/2, 1/4, 1/8, ... will yield codewords of lengths 1, 2, 3, ...

The model can be viewed as a block cellular automaton of the type discussed on page 460 , but on a 2D hexagonal grid. In general a block cellular automaton works by making replacements for overlapping blocks of cells on alternating steps. … On a 2D square grid, one can use overlapping 2×2 square blocks.

And in all cases black cells appear only in blocks that are an odd number of cells wide. (Any block in rule 73 consisting of an even number of black cells will evolve to a structure that remains fixed forever, as mentioned on page 954 .) The more complicated central region of the pattern grows 4 cells every 7 steps; the outer region consists of blocks that are 12 cells wide and repeat every 3 steps.

Block frequencies [in sequences] In any repetitive sequence the number of distinct blocks of length m must become constant with m for sufficiently large m . … Up to limited m nested sequences can contain all k m possible blocks, and can do so with asymptotically equal frequencies. … In both cases equal frequencies of blocks are obtained only for sequences of length exactly 2 j .

[Cellular automaton] rule emulations The network below shows which quiescent symmetric elementary rules can emulate which with blocks of length 8 or less. … But such a block corresponds in a sense to a horizontal slice through the cone of previous cell colors. … So this means that one can consider encodings based on blocks that have a kind of staircase shape—as in the rule 45 example shown.

Such systems in general take a string of elements and at each step replace blocks of these elements with other elements according to some definite rule. … The substitution system works by replacing blocks of elements at each step according to the rule shown.

The basic idea is that a block of 20 cells in the universal cellular automaton is used to represent each single cell in the cellular automaton that is being emulated. And within this block of 20 cells is encoded both a specification of the current color of the cell that is being represented, as well as the rule by which that color is to be updated.

No 2 × 2 or larger block of white squares can ever occur. … The first 2 × 2 block of black squares occurs at {14, 20} , the first 3 × 3 block at {1274, 1308} and the first 4 × 4 block at {7247643,10199370} . The densities of such blocks are respectively about 0.002, 2 × 10 -6 and 10 -14.