The entanglement can be evaluated in terms of sinuosity (S), defined as L/d, wherein d is the shortest distance between the two ends of a given fibre with the length L. The value of S for a perfectly straight fibre (S=1.0) increases upon increasing the degree of entanglement. Histograms of L, d and S values for randomly chosen fibres of SPspiral, (SPlinear)UV and (SPrandom)Vis are shown in Supplementary Fig. 12. The L of the above three SPs are widely distributed in the range of 100–1,500 nm, and the distribution showed no arguable difference before and after light irradiation. In contrast, the distribution of d displayed a great change before and after light irradiation. While the d of most SPspiral and (SPrandom)Vis fibres are in the range of 100–500 nm, those of (SPlinear)UV fibres are distributed in a wider range up to 1,200 nm due to extension. As a result, most of the (SPlinear)UV fibres have S values in the range of 1.0–3.0, which illustrates their extended form, whereas those of SPspiral and (SPrandom)Vis are more widely distributed in the range of 2–20, which illustrate the substantial difference in entanglement well.