  A thin thread of viscous fluid falling onto a moving belt generates a
surprising variety of patterns depending on the belt speed, fall height, flow
rate, and fluid properties. Here we simulate this experiment numerically using
the Discrete Viscous Threads method that can predict the non-steady dynamics of
thin viscous filaments, capturing the combined effects of inertia, stretching,
bending and twisting. Our simulations successfully reproduce nine out of ten
different patterns previously seen in the laboratory, and agree closely with
the experimental phase diagram of Morris et al.\ (2008). We propose a new
classification of the patterns based on the Fourier spectra of the longitudinal
and transverse motion of the point of contact of the thread with the belt.
These frequencies appear to be locked in most cases to simple ratios of the
frequency $\Omega_c$ of steady coiling obtained in the limit of zero belt
speed. In particular the intriguing `alternating loops' pattern is produced by
combining the first five multiples of $\Omega_c/3$.
