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The Hutchinson metric is a natural measure of the discrepancy between two images for use in fractal image processing. A neural network is described which can quickly calculate this metric. By combining this with the architecture previously described by the author for implementing the Markov operator of an iterated function system (IFS) on a neural network, a fast method is obtained for determining the distance between a target image and the invariant measure of a trial IFS. This has obvious applications to Barnsley's fractal image compression scheme