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this post was submitted on 05 Sep 2025
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it's unexpectedly symmetrical, although i guess the "harmonic" of the bicycle explains that.
Symmetrical up/down? Or do you mean almost periodic right to left?
well since it's a top-down diagram i guess you can say up/down. but right/left is probably more accurate.
I don't know. I expect it to be symmetrical in that direction. Why should it behave different tilting left than right? It being periodic is much more unexpected to me. It makes sense but, without really thinking about it, I would have expected it to be more chaotic.
It's entirely expected. The anomalies are going to be on the furthest left and right; Bikes that fall down right away or ones that stay up longest. The average would be the densest area - bikes that performed "okay." The symmetry is also an expected function with the only options for the wheel to turn being left or right.
If these were not standardized releases, meaning, the energy used to push the bike varied from one to the next - say, because a person was pushing them and not a machine with a defined load - then it explains the short vs. long distances, however that would be normalized even with a predefined load and look similar to this... just bigger distances.
Bikes aren't symmetrical though, with the drive-train to one side, so you'd think there'd be a more noticeable bias in one direction. Guess it's a very minor effect.
I dug up the actual paper (Cook, 2004) and it turns out the bicycle was symmetrical... and, in fact, entirely virtual.
It's a plot of a computer simulation, rather than records from a real-world physical experiment.
So the simulation has a lot of simplifications from reality, and the picture tells us more about the simulation model than it tells us about the real world. It is a pretty picture, though.
Here's the paper reference:
Cook, M. 2004. It takes two neurons to ride a bicycle.
(I couldn't get it from the Cook's Caltech site, but I found a copy elsewhere.)
The interesting thing in this situation is that it curved at all.
The fork is bend so the bike automatically counter-steers against gravity. As long as the speed is high and the wheels are spinning (centripetal/symmetry forces), it will tend to steer in a straight line. So the spinning wheel and the bend, makes the bike run upright. The bend has a name, but I forgot..