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> Are you talking about a random distribution of points on a line / square, or about rolling dice? Right, exactly. I made my comment in reply to the grandparen
by Osmium 11y ago
> Are you talking about a random distribution of points on a line / square, or about rolling dice?
Right, exactly. I made my comment in reply to the grandparent problem talking about dots on a screen. For a discrete distribution like a dice roll in the parent post it'd be a different matter. (I was going to edit my comment to clarify, but the edit window had expired.) Which serves to illustrate why it's important to be precise when talking about what distribution you're sampling.
Also, trying to run this experiment in practice is also problem even for dots on a screen, because eventually the finite display size of your dots will become an issue, as will floating point arithmetic (since you only really have a finite number of floats in a given range).
- eru 11y agoThanks for clarifying. > Also, trying to run this experiment in practice is also problem even for dots on a screen, because eventually the finite display size of your dots will become an issue, as will floating point arithmetic (since you only really have a finite number of floats in a given range). Yes, but that's not a problem for the theoretical analysis of fractal dimension. Uniformly placed dots do have a characteristic density and a relatively simple distribution of nearest neighbour distances. Even the clumpiness doesn't lead to scale invariant lumps. The lumps get absolutely bigger on bigger scales, but relatively smaller and smoother. It would be useful to do the analysis properly, though.