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But does the existence of this short description mean that picture (c) should not be considered random?
But what is perhaps still more striking is that the patterns of repeated regions seem to capture almost every regularity that we readily notice by eye—as well as some that we do not.
Traditional intuition might suggest that to do more sophisticated computations would always require more sophisticated underlying rules.
So to determine whether a particular square in the pattern is black or white, all one need do is to compute the corresponding binomial coefficient, and see whether or not it is an odd number.
Ordinary hashing would not let us do this.
And as data gets received by the brain such changes presumably do occur at least in some cells.
So how then does the proof of universality proceed?
So what does this mean about the computational capabilities of such systems?
So although this means that the particular type of approach we used to demonstrate the universality of rule 110 cannot immediately be used for rule 30 or rule 45, it certainly does not mean that these rules are not in the end universal.
And certainly in the picture on the facing page rule 110 does not seem to stand out.
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