@Danpiker@mathstodon.xyz on mathstodon.xyz
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Danpiker
@Danpiker@mathstodon.xyz ·Mar 25
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Craig S. Kaplan
@csk@mathstodon.xyz ·Mar 25
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@Danpiker@mathstodon.xyz 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.
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Grégoire Locqueville
@glocq@mathstodon.xyz ·Mar 25
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@csk@mathstodon.xyz
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@mathstodon.xyz
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Danpiker
@Danpiker@mathstodon.xyz ·Mar 26
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@glocq@mathstodon.xyz @csk@mathstodon.xyz these quadrilaterals need to be both equidiagonal and orthodiagonal.
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Bathsheba Grossman
@bathsheba@mathstodon.xyz ·Mar 27
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I feel like this is related to
https://www.nga.gov/artworks/61279-fish-and-scales
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kubi
@bikubi@mastodon.social ·Mar 25
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@Danpiker@mathstodon.xyz i just absentmindedly stared into the center of this one (where my cursor was sitting), and when i stopped the animation by removing the cursor I perceived an unusually intense "reverse motion optical illusion"... even the text box i'm typing this in seems to spiral :)
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myrmepropagandist
@futurebird@sauropods.win ·Mar 26
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@Danpiker@mathstodon.xyz
Did 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?
https://www.youtube.com/watch?v=ldxFjLJ3rVY
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Danpiker
@Danpiker@mathstodon.xyz ·Mar 26
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@futurebird@sauropods.win 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.
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alg0w
@alg0w@social.vivaldi.net ·Mar 25
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@Danpiker@mathstodon.xyz Unbelievably smooth transitions for squares.