mechanisms in programs and nature
Salient points / claims:
- there are 3 mechanisms for generating randomness:
- from the environment (i.e. get it from some place else)
- from sensitivity to initial conditions (chaos)
- the d.i.y. randomness intrinsic to simple programs
- the third one is new
- The central column of Rule 30 is what Mathematica uses for its RNG, and it's really really really random.
- more about constraints - (what was the story here?)
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I think that mechanisms 2 and 3 are actually the same. e.g. think of rule 30, for which the middle column is very random. A given cell, say 50 steps down, has a "window" 100 wide on the first row, which is the cell's "initial condition". This initial condition gets more complex with every timestep, in just the same way as reading off the digits of an irrational number does (which Wolfram convincingly relates to essentially all chaotic phenomena, if I read him correctly). Perhaps the fact that the new parts being added are all zeros is throwing us a red herring here? But "all we're adding is zeros" is not the same as "we're not adding anything", which is what Wolfram is implying. Marcus Frean |
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