An unsupervised competitive learning rule is introduced for topology-preserving map formation. The rule, called vectorial boundary adaptation rule (VBAR), achieves a ''maximally''-ordered map by performing local weight updates only: hence, contrary to Kohonen's self-organizing map (SOM) algorithm, no neighborhood function is needed. We formalize VBAR's learning dynamics and show by simulations that it converges in a completely different way from the SOM algorithm. Our rule is aimed at achieving an equiprobable quantization of the input space (unconditional information-theoretic entropy maximization). Due to this property, we argue that VBAR is able to generate a ''sparse-distributed'' representation. Finally, we argue that entropy maximization is a plausible computational principle for topology-preserving map formation and that VBAR is a minimal assumption rule in this respect. (C) 1997 Elsevier Science Ltd.