alt.hn

1/11/2025 at 10:25:37 PM

Arnold's Cat (2018)

 http://gerdbreitenbach.de/arnold_cat/cat.html

by bradly

1/16/2025 at 4:54:06 AM

Managed to time-sync the frame transitions to an old Juno Reactor album and i'm right back in some weird MTV esque vibe like I'm watching Beavis and Butthead or Duckman or something.

by bnetd

1/15/2025 at 8:21:25 PM

The page doesn't say why matrices need to have whole-number (really just integer) entries, but I'd suspect it's because bad approximations to non-integer rationals accumulate sufficiently to make the recurrence unrecognizable.

by JadeNB

1/15/2025 at 8:34:18 PM

It says that the underlying action is on the torus (R/Z)^2. If the entries of the matrix are not integers, do we have a well defined action on the torus? It seems to me that the answer is no because Z^2 would not be invariant by the action.

by pepinator

1/16/2025 at 3:15:10 AM

One can still define a map by taking the fractional part of the matrix-vector product, but the resulting map won't be continuous (with respect to the topology of the torus). In addition, if one wants the map be a homeomorphism (continuous with continuous inverse) then the determinant must have absolute value 1.

by kkylin

1/15/2025 at 8:45:37 PM

> It says that the underlying action is on the torus (R/Z)^2. If the entries of the matrix are not integers, do we have a well defined action on the torus? It seems to me that the answer is no because Z^2 would not be invariant by the action.

Ah, good point.

by JadeNB

1/16/2025 at 3:03:59 AM

Cool, though I didn't understand it at all

by 01HNNWZ0MV43FF