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He argued that the best scientific model is one that minimizes this complexity—which with probabilities 0 and 1 is equivalent to minimizing the number of nodes in the network.
In the 1D case of page 460 , the blocks that are replaced consist of pairs of adjacent cells with two different alignments.
In flowering plants, cell division normally occurs around the edge of a region of size 0.2-1 mm containing many tens of cells.
But even with a 10×10 array of black and white squares, the number of possible patterns is already 1,267,650,600,228,229,401,496,703,205,376.
In both rules shown the cell itself and its nearest neighbors enter with weight 1.
For the model does not say that such sequences are impossible—it merely says that they should occur only about 1% of the time.
The basic idea is to translate the rule for a given cellular automaton into a formula that depends on three variables a 1 , a 2 and a 3 whose values correspond to the colors of the three initial cells.
And if one computes even a function like 1/x almost any digit in x will typically have an effect on almost any digit in the result, as the pictures on the facing page indicate.
And this means for example that the outcome of a million steps of evolution for either of the cellular automata on the left is now determined by just 20 steps of evolution, where 20 is the length of the base 2 digit sequence of the number 1,000,000.
Mathematica works by taking its input and repeatedly applying transformation rules—a process which normally reaches a fixed point that is returned as the answer, but with definitions like x = x + 1 ( x having no value) formally does not.
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