Search NKS | Online
71 - 80 of 195 for Through
Each connection in each network has a certain probability associated with it, and the model takes sequences of black and white squares to be generated by tracing paths through the networks according to these probabilities.
Cases (c) through (f) are similar,
An example of a mobile automaton.
The equation has many solutions, but all of them satisfy the constraint that the variables x 1 through x 4 must encode possible initial conditions and evolution histories for rule 110.
Because only a single element is removed at each step, the systems effectively just cycle through all elements, replacing each one in turn.
0 through 9.
But looking through this book it becomes clear that even a program that may have extremely simple rules will often be able to generate pictures that have striking aesthetic qualities—sometimes reminiscent of nature, but often unlike anything ever seen before.
Indeed, it seems that the best approach is essentially just to search through many different partial differential equations, looking for ones that turn out to show complex behavior.
For if the only way for intrinsic randomness generation to occur was through very complicated sets of rules, then one would expect that this mechanism would be seen in practice only in a few very special cases.
But with a larger number of components it becomes progressively easier for randomness to be generated through intrinsic randomness generation.
So in all of these cases the randomness one sees cannot reasonably be attributed to randomness that is introduced from the environment—either continually or through initial conditions.