alt Hacker NewsCan you clarify what the “potential field” actually is? The text is not really precise, and the little interactive tool has the very curious property that I can set all the potentials to 0 and I don’t get all zeros in the magic hexagon.
I would guess that the smooth mountain-looking structure come from a very simple observation: a gadget consisting, in potential space, of a 2 surrounded by a ring of 6 1’s fully cancels at the center and in the ring immediately around the center and leaves a nice pattern of +1 and -1 residuals in the ring around it. I suspect that, fairly generally, as you try to build out small numbers around the outside of the magic hexagon, you end up with a large pile of things like this in the center, and a sum, even a very noisy one, of things that even vaguely Gaussians, tends to produce Gaussians. (That’s the central limit theorem.)
Apologies for the confusion - the playground had a typo (7 instead of 8) which is fixed now. Now it works as you would expect, and zeroed potentials correspond to a zeroed hexagon.
The "wide ring" gadget is an interesting idea. I think it will be linear pyramids and not gaussian. A set of these gadgets can also form a basis, and in such a different basis the potential fields may look very different - almost flat, perhaps?..