This is a long shot, but I'm looking for a particular article that I once read, and I'm trying to find it again. It deals with a certain Cantor set in the plane. The set could be written as something like this: $$C=\sum_{n=2}^\infty\frac{1}{n^2}\exp\frac{2\pi i\mathbb Z}{n}.$$ In other words, $C$ contains all sums of series whose $n$th term is an $n$th root of unity multiplied by a quickly decreasing sequence of scales. The scales might not have been $1/n^2$; that's just a guess. The set is composed of two side-by-side blobs, each of which is a triangle of three smaller blobs, each of which is a diamond of four blobs, each of which is a ring of five blobs, each of which is a ring of six blobs, etc. It's sort of a disconnected multi-gasket... fractal thingy.
The article definitely included a computer-generated diagram of $C$, maybe two or three. I want to say that it had a preprint on arXiv, but I'm not sure. I don't think it was particularly focused on $C$, so the definition and the diagram(s) would occur somewhere in the middle of the article, and the abstract probably doesn't mention $C$ at all.
I don't remember anything else about the context, including the article's mathematical content! I know why I'm suddenly interested in $C$: it's a seemingly rare example of a Cantor set that doesn't contain any "corner point": a point whose Bouligand tangent cone is contained in an open half-space. But I don't remember why the author(s) introduced the example in the first place. When I saw the article, I was just searching for Cantor sets with interesting geometry, not for any particular result.
Does anyone know the reference I'm looking for? If not, maybe there are suggestions on how one would search for such a thing? Can you divine what the context must have been?
Victory! The winning query was "cantor" + "regular polygon".