When straining polyurethane elastomers (PUEs), it is often observed that the long-period peak of the small-angle X-ray scattering (SAXS) does not shift normally. An explanation is indicated for some PUEs in the real-space chord distribution. It exhibits a sequence of constant long-period bands. The band positions form a Fibonacci sequence. This relates to the underlying chemical synthesis by polyaddition of hard and soft modules, indicating a nearly quasiperiodic setup in sequences of stringed hard domains. These sequences appear to be the probes provided by SAXS for the study of morphology evolution in such PUEs. Should a regular-as-possible arrangement of physical crosslinks optimize a property of the material, then in the synthesis the mole fraction nH of hard modules should be chosen to be nH = [tau]/(1 + [tau]) [asymptotically equal to] 0.62, where [tau] is the golden ratio.