Search NKS | Online
211 - 220 of 320 for While
But while the statement of the proof makes extensive use of concepts from areas like set theory, it seems quite likely that in the end a version of it could be given purely in terms of Peano arithmetic.
If too little is specified, there may be many possible solutions, while if too much is specified there may be no consistent solution at all.
These elements can then overlap while not affecting the result.
For rule 90 the combination c can be specified as {{1, 0, 1}} , while for rule 150R it can be specified as {{0, 1, 0}, {1, 1, 1}} .
But after a while I began to suspect that many of the most important and fundamental questions that I was encountering were quite independent of the abstruse details of these fields.
And after a while I realized that if there was going to be any dramatic progress made, I was the one who was going to have to make it.
For while class 4 is above class 3 in terms of apparent complexity, it is in a sense intermediate
Rare examples of borderline cellular automata that do not fit squarely into any one of the four basic classes described in the text.
But while definitions of this type have a certain conceptual appeal, they are not likely to be useful in discussions of randomness in nature.
Some of these structures remain stationary, like those at the bottom of the first page while others move steadily to the right or left at various speeds.
And in the end it is, I suspect, just that some of the possible underlying genetic programs happen to produce complex patterns, while others do not.