I first met Stu Whittington at a Chemical Institute of Canada Symposium on Computational and Mathematical Chemistry, Saskatoon, Canada, June 1986. At that symposium I presented the then unsolved problem of the Frisch-Wasserman-Delbruck conjecture—the longer a random curve is in 3-space, the more likely that it is knotted. After my talk, Stu came up and said—“Do you know about the Kesten Pattern Theorem?” This was a career-changing event for each of us, the beginning of a long and very productive friendship and collaboration. This talk will traverse some of the random trails that Stu and I have been down.