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The basic idea is to encode the list of values of all the registers in the multiregister machine in the single number given by
RMEncode[list_] := Product[Prime[j]^list 〚 j 〛 , {j, Length[list]}]
and then to have this number be the value at appropriate steps of the first register in the 2-register machine.
The weather
Almost all the intricate variations of atmospheric temperature, pressure, velocity and humidity that define the weather we see are in the end determined by fairly simple underlying rules for fluid behavior.
Note that if all blocks in a cyclic tag system with n blocks have lengths divisible by n , then one can tell in advance on which steps blocks will be added, and the overall behavior obtained must correspond to a neighbor-independent substitution system.
There continued to be slow progress in finding specific large primes; 2 31 - 1 was found prime around 1750 and 2 127 - 1 in 1876. ( 2 2 5 + 1 was found composite in 1732, as have now all 2 2 n + 1 for n ≤ 32 .)
All parts of the Mandelbrot set are known to be connected.
For any q the maximum h[q, n] 1 occurs when all p[i] k -n .
Usually this mapping is contractive, so that not all the states which appear as input to the mapping can also appear as output.
Whether a pattern with all the properties expected in DLA is produced seems to depend in some detail on the rules for the gray cells.
To do this explicitly for all possible p that can occur would however entail having infinitely many new rules.
Another result that has been derived is that the average total number m[n] of edges of all faces around a given face with n edges is 7n + 3 + 9/(n + 1) .