We present multicolour photometry of the M8.5V ultracool dwarf `pulsar' TVLM 513-46546 (hereafter TVLM 513) obtained with the triple-beam photometer ULTRACAM. Data were obtained simultaneously in the Sloan-g' and Sloan-i' bands. The previously reported sinusoidal variability, with a period of 2 h, is recovered here. However, the Sloan-g' and Sloan-i' light curves are anticorrelated, a fact which is incompatible with the currently proposed starspot explanation for the optical variability. The anticorrelated nature and relative amplitudes of the optical light curves are consistent with the effects of persistent dust clouds rotating on the surface of the star. In the absence of other plausible explanations for the optical variability of TVLM 513, it seems likely that dust cloud coverage combined with the rapid rotation of TVLM 513 is responsible for the optical variability in this object. However, crude modelling of a photosphere with partial dust cloud coverage shows that the anticorrelation can only be reproduced using cooler models than the literature temperature of TVLM 513. We suggest this discrepancy can be removed if more dust is present within the photosphere of TVLM 513 than theoretical model atmospheres predict, though a definitive statement on this matter will require the development of self-consistent models of partially dusty atmospheres. Based on observations made at the European Southern Observatory, Paranal, Chile (ESO programme 079.C-0686). E-mail: S.Littlefair [at] sheffield.ac.uk (S[dot]Littlefair[at]sheffield[dot]ac[dot]uk)