4 ms·

Ended up playing with the animation for a while, this is probably nothing new but just thought I'd share a funny quirk I discovered. If you plug in the fibonac

by iooi 14y ago

Ended up playing with the animation for a while, this is probably nothing new but just thought I'd share a funny quirk I discovered. If you plug in the fibonacci sequence for the time, you get symmetrical strengths and phases (except for the first term): For (0 1 1 2 3 5 8 13 21 34 55 89 144 233 377 610) you get: 99.74 77.77:51.4 53.46:82.8 39.97:104.3 32.41:121.8 27.98:137.3 25.39:152 24.03:166.2 23.62:180 24.03:-166.2 25.39:-152 27.98:-137.3 32.41:-121.8 39.97:-104.3 53.46:-82.8 77.77:-51.4 Formatting magic: 99.74 1 - 77.78 51.4 2 - 53.46 82.8 3 - 39.97 104.3 4 - 32.42 121.8 5 - 27.98 137.3 6 - 25.39 152 7 - 24.03 166.2 8 - 23.63 180 7 - 24.03 -166.2 6 - 25.39 -152 5 - 27.98 -137.3 4 - 32.42 -121.8 3 - 39.97 -104.3 2 - 53.46 -82.8 1 - 77.78 -51.4 It works for all sequence lengths I've tried, although the app starts rounding off when you start getting in the hundreds.. not that it matters in this case. Couldn't find any relationship between the first constant and the pairs, nor any relationship between the ratio of the pairs. Just something interesting.

napoleond 14y ago
Without wanting to quell any enthusiasm (or cause too much confusion), it's probably worth pointing out that any real-valued time-series input will result in a similarly symmetric pattern. I can't explain why that's true in a way that makes sense with the analogy used here, but it is.
kalid 14y ago
Awesome, glad you were able to explore! As the other reply mentioned, it actually turns out that all real (1d) signals are symmetric. The key reason is in order for a circular path to stay on the real axis, it needs to be combined with another path rotating the opposite way, so their sum will stay on the x-axis. The "opposite" rotation can be a negative frequency (1Hz vs -1Hz) or a very fast positive frequency (if you have a 12-hour clockface, 1 hour backwards = 11 hours forward, aka -1 (mod 12) = 11 (mod 12)). I'd like to explore this in the follow-up, glad you discovered it.

by iooi 14y ago

napoleond 14y ago

Without wanting to quell any enthusiasm (or cause too much confusion), it's probably worth pointing out that any real-valued time-series input will result in a similarly symmetric pattern. I can't explain why that's true in a way that makes sense with the analogy used here, but it is.

kalid 14y ago

Awesome, glad you were able to explore! As the other reply mentioned, it actually turns out that all real (1d) signals are symmetric. The key reason is in order for a circular path to stay on the real axis, it needs to be combined with another path rotating the opposite way, so their sum will stay on the x-axis. The "opposite" rotation can be a negative frequency (1Hz vs -1Hz) or a very fast positive frequency (if you have a 12-hour clockface, 1 hour backwards = 11 hours forward, aka -1 (mod 12) = 11 (mod 12)). I'd like to explore this in the follow-up, glad you discovered it.