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For any given rule one can define the neighborhood size s to be the largest block of cells that is ever needed to determine the color of a single new cell.
(Many programs nevertheless contain variables that need to be assigned their values before the programs are run—as can be done for example with Block[{k = 2}, program] .
And thus, for example, in rule 22, changing the color of a single cell has no effect after even one step if the cell has a block on either side.
In the immune system blocks of DNA—and joins between them—are selected at random by microscopic chemical processes when antibodies are formed.
Post's tag systems differ from mine in that his allow the choice of block that is added at each step to depend only on the very first element in the sequence at that step (see however page 670 ).
As shown in the pictures below, when started from blocks of certain sizes this rule yields complex patterns—although nothing like this was noted in 1967.
With rules in this form the network update is simply
NetStep[rule_, net_]:= Block[{new}, net /. rule /. new[n_] n + Apply[Max, Map[First, net]]]
Note that just as we discussed for strings on page 1033 the direct use of /. here corresponds to a particular scheme for applying the update rule.
In 1949 Claude Shannon and Robert Fano devised a systematic way to assign codewords based on probabilities of blocks.
Much like example (c) on page 83 there are m + 1 distinct blocks of length m , and with f = Floor[(1 - 1/ √ 2 )(# + 1/ √ 2 )] & the n th element of the sequence is given by f[n + 1] - f[n] (see page 903 ).
A number is said to be "normal" in a particular base if every digit and every block of digits of any length occur with equal frequency.