We present in this paper a variation of the self-organizing map algorithm where the original time-dependent (learning rate and neighborhood) learning function is replaced by a time-invariant one. The resulting self-organization does not fit the magnification law and the final vector density is not directly proportional to the density of the distribution. This lead us to introduce the notion of motivated self-organization where the self-organization is biased toward some data thanks to a supplementary signal. From a behavioral point of view, this signal may be understood as a motivational signal allowing a finer tuning of the final self-organization where needed. We illustrate this behavior through a simple robotic arm setup.