Search NKS | Online
151 - 160 of 230 for Position
Nevertheless, following our discussion of randomness in the previous section , we are now in a position to consider how the notion of complexity might be formally defined.
The comparative sparsity of dark blocks is a consequence of the fact that at any given position a dark block can occur in only one of the 16 cases shown.
Each nerve cell fires and yields black output only if the inputs it gets from certain fixed positions match a particular template.
In analogy to the previous page , the positions of white cells at the bottom of the rule 94 picture correspond to even numbers, on the left in rule 62 to multiples of 3, in rule 190 to multiples of 4, and in the center column of rule 129 to powers of 2.
The left part of each cellular automaton configuration emulates the actual evolution of the Turing machine; a specification of which rules should be applied at each step is progressively fetched from the right and delivered to the position of the head.
Four centuries ago we learned for example that our planet does not lie at a special position in the universe.
Each step in its evolution can be implemented using
LifeStep[a_List] := MapThread[If[(#1 1 && #2 4) || #2 3, 1, 0]&, {a, Sum[RotateLeft[a, {i, j}], {i, -1, 1}, {j, -1, 1}]}, 2]
A more efficient implementation can be obtained by operating not on a complete array of black and white cells but rather just on a list of positions of black cells.
If each node in a network is associated with a point in spacetime, then one slightly peculiar feature is that every such point would have an associated string—something like an encoded position coordinate.
In 1887, however, Heinrich Bruns showed that there could be no such quantities expressible as algebraic functions of the positions and velocities of the bodies (in standard Cartesian coordinates). In the mid-1890s Henri Poincaré then showed that there could also be no such quantities analytic in positions, velocities and mass ratios.
For light level—as with color constancy—this is presumably achieved by responding only to differences between levels at different positions.