So... any idea what is the source of the pattern that pops up here? :)

Plain old interference? It becomes more obvious when you replace aspect with a slider, e.g. viewof aspect = html`<input type=range step=.000001 value=.201788>`

A less brute force method is to use the convergents of the continued fraction. https://www.wolframalpha.com/input/?i=continued+fraction+for+sqrt%283%29 [1; 1, 2] = 5/3 [1; 1, 2, 1] = 7/4 [1; 1, 2, 1, 2] = 19/11 [1; 1, 2, 1, 2, 1] = 26/15 [1; 1, 2, 1, 2, 1, 2] = 71/41 [1; 1, 2, 1, 2, 1, 2, 1] = 97/56 [1; 1, 2, 1, 2, 1, 2, 1, 2] = 265/153

Interesting, although the higher values have a "plain" diamond shape and not this semi-regular tiling that 3/2 seems to have: https://observablehq.com/d/356853f2f052fc18

@jrus The idea here is that I can make an informed decision regarding the tradeoff of width vs error. E.g., if I had originally planned to not go below a width of 100px or above 250px, I could check here if there's a good fit close to (but outside) these bounds that would justify exceeding them. ... Although I should probably take the ratio of width to error into account as well. 🤔 Or were you refering to something else?

You’ll notice that the list of fractions I posted have numerators corresponding to all of the least-error dots on your plots. Looking at the convergents is a way to get a list of all the best possible choices you could make.

@jobleonard You might also like this one: https://observablehq.com/@harrystevens/function-iterator