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"Uniformly distributed" doesn't just mean sampled from a uniform distribution. It also means evenly spaced, as is the case here. It reminds me of Poisson dis
by mkl 1y ago
"Uniformly distributed" doesn't just mean sampled from a uniform distribution.
It also means evenly spaced, as is the case here. It reminds me of Poisson disk sampling. Here's an article about Poisson disk sampling that uses "uniform" in the sense the author is, and also compares to the uniform probability distribution: https://medium.com/@hemalatha.psna/implementation-of-poisson-disc-sampling-in-javascript-17665e406ce1 https://medium.com/@hemalatha.psna/implementation-of-poisson...
- gpm 1y agoReally the germane point isn't that it isn't specifically a uniform distribution, but that there is clearly structure to the distribution of those points. The locations are visibly not a set of IID random variables, because IID random variables don't space out that... uniformly. That said, while I agree "uniform" not followed by an inflection of "distribution" has many other meanings, I do not agree that it the context of math, in a context where there is a standard uniform distribution, and without other relevant context, "uniformly distributed" can properly be understood to mean anything other than distributed via the standard uniform distribution.
- pepinator 1y agoThe notion of being uniformly distributed has a very specific meaning in mathematics [1]. If you don't believe me, maybe you believe Tao [2]. [1] https://en.m.wikipedia.org/wiki/Equidistribution_theorem https://en.m.wikipedia.org/wiki/Equidistribution_theorem [2] https://terrytao.wordpress.com/2020/01/25/equidistribution-of-syracuse-random-variables-and-density-of-collatz-preimages/ https://terrytao.wordpress.com/2020/01/25/equidistribution-o...
- deleted 1y ago[deleted]