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.
GrΓ©goire 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
Bathsheba GrossmanI feel like this is related to
https://www.nga.gov/artworks/61279-fish-and-scales
https://www.nga.gov/artworks/61279-fish-and-scales
ππππππ@Danpiker π nice
kubi
alg0w
myrmepropagandistDid you see the 3 blue 1 brown breakdown about the Esher painting?
This isn't the same but it feels similar.
Can this get as small as we like?
How (and why) to take a logarithm of an image
@futurebird Yes - it's a very nice video. There is indeed a link - complex analysis. One way of generating these square tilings is via discrete harmonic functions.
robinhouston@Danpiker I like these very much! Have you explained how you made them anywhere?
@robinhouston Thanks! I'll try and do a little write-up soon.
RobJLow@Danpiker @robinhouston Ooh, I'd definitely like to see that. I've only worked out how to do a baby version of this kind of thing that's 'flat' (so to speak), where the centres of all the squares are fixed on a square grid.
Owen Maresh@Danpiker would you be willing to share how you make these? I'm either interested in manufacturing theta series over the centers of the squares weighted their areas or the vertices already in this image, and seeing how those theta series change as these are transformed.