A prototype solving the Shortest Path Problem (SPP) by a parallel message-passing algorithm is presented. The system, an OCCAM program running on a transputer board hosted by a PC, implements a known distributed algorithm for the SPP, based on the 'diffused computation' paradigm. A new parallel message-passing architecture is proposed, built upon a static packet-switching network with a fractal topology. The recursive, unlimited network, features an interesting property when applied to four-link processors (like transputers): it's decomposable, at any hierarchical level, in four-link modules or supernodes. Labelling and routing algorithms for the network, exploiting self-similarity, are described. Experimental results, obtained with a single transputer solving irregular random graphs (up to 256 nodes) are presented, showing a time complexity function growing linearly with the total number of arcs.