For what happens is that each block in effect independently acts like a system of limited size. The right-hand neighbor of the rightmost cell in any particular block is the leftmost cell in the next block, but since all the blocks are identical, this cell always has the same color as the leftmost cell in the block itself. … It turns out that no block of any size gives a period of exactly two steps, but blocks can be found for all larger periods at least up to 15 steps.

Another common approach to data compression is based on forming blocks of fixed length, and then representing whatever distinct blocks occur by specific codewords. … In each case the input is taken to be broken into blocks of length 3. … Examples of Huffman coding based on blocks of length 3.

When a larger number of distinct blocks occur, longer codewords must inevitably be used. But compression can still be achieved if the codewords for common blocks are sufficiently much shorter than the blocks themselves. … Huffman encoding with blocks of length 6 applied to patterns produced by cellular automata.

Like block encoding, pointer-based encoding can also be extended to two dimensions. … Each image is broken into 3×2 blocks, and codewords are then assigned to these blocks using the Huffman scheme. … Cellular automaton rule 30, and the 3×2 blocks which appear in large patterns generated by it.

With two possible colors and blocks of size two the only kinds of block cellular automata that conserve the total number of black cells are the ones shown in the second set of pictures—and all of these exhibit rather trivial behavior. An example of a block cellular automaton. … Block cellular automata with two possible colors and blocks of size two that conserve the total number of black cells (the last example has this property only on alternate steps).

The basic idea of a block cellular automaton is illustrated at the top of the next page . At each step what happens is that blocks of adjacent cells are replaced by other blocks of the same size according to some definite rule. And then on successive steps the alignment of these blocks shifts by one cell.

In both the rules shown on the facing page , the only replacement specified is for the block . … If one had replacements for blocks such as , or then these could overlap. … If a rule involves replacements for several distinct blocks, then to avoid the possibility of interference one must require that these blocks can never overlap either themselves or each other.

In an ordinary tag system, one does not know in advance which of several possible blocks will be added at each step. … In the simplest case there are two possible blocks, and the rule simply alternates on successive steps between these blocks, adding a block at a particular step when the first element in the sequence at that step is black. … The rule can be summarized just by giving the blocks to be used in each case, as shown in the rule summary.

The point is that these initial conditions in effect contain only blocks for which rule 126 behaves like rule 90. … And with an appropriate form for these blocks what one finds is that the configuration of blocks evolves exactly according to rule 90. The fact that both individual cells and whole blocks of cells evolve according to the same rule then means that whatever pattern is A demonstration of the fact that in rule 90 blocks of cells can behave just like individual cells.

The idea is just to set up initial conditions that correspond to the blocks that appear in the rule for whatever cyclic tag system one wants to emulate. The necessary initial conditions consist of repetitions of blocks of cells, where each of these blocks contains a pattern of localized structures that corresponds to the block of elements that appear in the rule for the cyclic tag system. The blocks of cells are always quite complicated—for the cyclic tag system discussed in most of this section they are each more than 3000 cells wide—but the crucial point is that such blocks can be constructed for any cyclic tag system.