Line integral convolution (LIC) is a powerful method for computing directional textures from vector data. LIC textures can be animated, yielding the effect of flowing motion. Both, static images and animation sequences are of great significance in scientific visualization. Although an efficient algorithm for computing static LIC textures is known, the generation of animation sequences still requires a considerable amount of computing time. In this paper we propose an algorithm for computing animation sequences on a massively parallel distributed memory computer. With this technique it becomes possible to utilise animated LIC for interactive vector field visualization. To take advantage of the strong temporal coherence between different frames, parallelization is performed in image space rather than in time. Image space coherence is exploited using a flexible update and communication scheme. In addition algorithmic improvements on LIC are proposed that can be applied to parallel and sequential algorithms as well.