Danpiker
Craig S. Kaplan@Danpiker I've seen still images (and animations?) of these sorts of arrangements of squares for a while now, and I still don't believe they're possible.
Grégoire Locqueville@csk
The following toot helped me figure it out partially:
https://mathstodon.xyz/@Danpiker/116289884555776002
You need a tiling of the plane by "anchor" quadrilaterals,
where an anchor quadrilateral is a quadrilateral Q such that there is a continuum of squares whose each side passes through a vertex of Q.
Now I'm not sure yet what characterizes anchor squares...
Danpiker (@[email protected])
Attached: 1 image @[email protected] It is possible to keep it clean at the origin