despite having a phd in nonlinear dynamics, I struggle to wrap my head around most of this stuff... but I always found is deeply fascinating. In one system I s

despite having a phd in nonlinear dynamics, I struggle to wrap my head around most of this stuff... but I always found is deeply fascinating. In one system I studied we had a sequence of period doublings, which followed one of the feigenbaum constants[1] seeing this happen in the lab, and subsequently seeing it numerically, and uncovering the analytics behind it was a worthy use of 6 years --- [1] https://en.wikipedia.org/wiki/Feigenbaum_constants https://en.wikipedia.org/wiki/Feigenbaum_constants