I've used a similar trick for decades: for example I put it in the code for my Hypnocube (www.hypnocube.com) product in 2005 (Hypnocube). I used it in games and digital art projects before (and after) that.
For embedded or low resource computing, sin/cos may be expensive, so I use a table based fixed point version. I pick the table to have size power of 2, making lots of things easier. Then to make time wrap, I use a large power of 2, which is exactly the same as this trick, with base 10 replaced with base 2 (and using fixed point math).
You also hit problems where delta times can go negative, so those also need to be max time aware. In short, I always make a timing module, it tracks time (and stretches it as needed), and doles out a few things used everywhere: a delta frame time, a large time (say 64 bits as ns for 584 year wraparound), and a capped time (say 16 or 24 bits) to use in places where you know the wrap amount and still give space for computations not to overflow.
As far as I know the Hypnocube never repeats nor does anything flicker at any time due to bad wraparounds. But that took work to ensure.
I remember seeing Hypnocube references and your site probably around 2005 or 2006, but it was so far beyond me at the time I just wrote it off as "cool OK". YouTube wasn't quite what it is today so I never did get to see what it looks like in motion. Today I assume similar things can be done extraordinarily cheap and easily but I still have no idea how. I'm not motivated enough right now to ask, but I just wanted to thank you for giving younger-me's friends something exciting to talk about for a short while.
For embedded or low resource computing, sin/cos may be expensive, so I use a table based fixed point version. I pick the table to have size power of 2, making lots of things easier. Then to make time wrap, I use a large power of 2, which is exactly the same as this trick, with base 10 replaced with base 2 (and using fixed point math).
You also hit problems where delta times can go negative, so those also need to be max time aware. In short, I always make a timing module, it tracks time (and stretches it as needed), and doles out a few things used everywhere: a delta frame time, a large time (say 64 bits as ns for 584 year wraparound), and a capped time (say 16 or 24 bits) to use in places where you know the wrap amount and still give space for computations not to overflow.
As far as I know the Hypnocube never repeats nor does anything flicker at any time due to bad wraparounds. But that took work to ensure.