Search NKS | Online
41 - 50 of 89 for Equal
(a) is unary, in which any given number is represented by a sequence of cells whose length is equal to that number.
But the crucial point is that because of the way the system was constructed there is nevertheless a simple formula for the color of each cell: it is given just by a particular digit in the number obtained by raising the multiplier to a power equal to the number of steps.
[Enumerating] possible expressions
LeafCount[expr] gives the number of symbols that appear anywhere in an expression, while Depth[expr] gives the number of closing brackets at the end of its functional representation—equal to the number of levels in the rightmost branch of the tree representation.
But the point is that when the initial number of black and white cells is exactly equal—corresponding to a phase transition point—a typical configuration of rule 184 will contain domains with a nested distribution of sizes.
As one simple example, consider a model in which all possible sequences of black and white squares are supposed to occur with equal probability.
From the point of view of statistical analysis, a sequence is perfectly random if it is somehow consistent with a model in which all possible sequences occur with equal probability.
Equal (if and only if) is common in more mathematical settings, while Xor is widespread in discrete mathematics.
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.
And in the late 1980s, building on work of mine from 1984 (described on page 276 ), James Crutchfield made a study of such models in which he defined the complexity of a model to be equal to -p Log[p] summed over all connections in the network.
(For an operator system such a model can have elements which are simply equivalence classes of expressions equal according to the axioms.)