Another pretty hypothesis blown
May. 6th, 2011 11:58 pm![[personal profile]](https://www.dreamwidth.org/img/silk/identity/user.png){kind=small}
mmcirvinYeah, using the correct distribution makes my results seem much less impressive. I'm actually not sure why they seemed to work as well as they did, using the Poisson. The graph for the Day and Night CA now makes sense, though.
It's the binomial distribution, because a pixel is either alive or dead; the positions of live pixels are necessarily anticorrelated by the fact that a pixel can't be doubly alive. You can see the Poisson is wrong because it would predict nonzero probabilities for more than eight live neighbors.
Anyway, it seems now like the presence of attracting fixed points is actually not so bad, as long as the attraction isn't too strong. That suggests that the effect of the stochastically modeled background is not quite as strongly predictive as my initial results implied. Curiously, the seemingly spot-on calculations I got for the densities in Serviettes and 3-4 Life are no longer correct, unless you tilt the identity line up to a slope of about 1.2 (which would correspond to a fudge factor that kills 1/6 of the live pixels in each step). Yeah, not really buying it...
Maybe the reason the Poisson distribution seemed to be working better than the binomial was that I was effectively sneaking in some of the additional positional correlations in the real-world CA. The difference between Poisson and binomial distributions would, I think, be a slight bias toward greater numbers of live neighbors than in a random distribution.
It's the binomial distribution, because a pixel is either alive or dead; the positions of live pixels are necessarily anticorrelated by the fact that a pixel can't be doubly alive. You can see the Poisson is wrong because it would predict nonzero probabilities for more than eight live neighbors.
Anyway, it seems now like the presence of attracting fixed points is actually not so bad, as long as the attraction isn't too strong. That suggests that the effect of the stochastically modeled background is not quite as strongly predictive as my initial results implied. Curiously, the seemingly spot-on calculations I got for the densities in Serviettes and 3-4 Life are no longer correct, unless you tilt the identity line up to a slope of about 1.2 (which would correspond to a fudge factor that kills 1/6 of the live pixels in each step). Yeah, not really buying it...
Maybe the reason the Poisson distribution seemed to be working better than the binomial was that I was effectively sneaking in some of the additional positional correlations in the real-world CA. The difference between Poisson and binomial distributions would, I think, be a slight bias toward greater numbers of live neighbors than in a random distribution.