[gpm]

> The points look quite uniformly distributed to me. If I squint, then maybe I can see some structure, but it's hard to describe and I could be imagining it.

It doesn't, these points look like what happens if you ask someone who doesn't know what a uniform distribution looks like to generate a uniformly distributed set of points though.

Here's what an actual uniform distribution looks like... much less "uniform": https://claude.ai/public/artifacts/00549caf-2ec1-4803-b909-6...

Credit to the book "Struck By Lightning" for making me aware of this fact, many years ago now. Disclaimer that the author is a family friend.

Edit: I misunderstood what was being plotted in the article, and as a result had claude plot random instead of evenly spaced X coordinates. It doesn't change my point, but this version has the appropriate distribution to compare to (evenly spaced x, uniformly randomly y coordinates): https://claude.ai/public/artifacts/a04a3023-25d3-4d99-889d-a...

[mkl]

"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...

[gpm]

Really 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]

The 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

[2] https://terrytao.wordpress.com/2020/01/25/equidistribution-o...

[willrftaylor]

For what it's worth, I thought "uniform" was a fine description - as you zoom out, the pattern looks more organised and less random. That is a property of uniform distributions.

https://bookdown.org/kevin_davisross/probsim-book/sec-linear...

[pepinator]

Irrational rotations of a torus are uniformly distributed and closely resemble the image from the blog. The images you linked, on the other hand, are random sequences with positive entropy (which are also uniformly distributed). Confusing these two things is what happens when someone without the necessary expertise tries to sound smart.

[WithinReason]

The author invented a new low discrepancy sequence generator