Artificial Intelligence has looked into biological systems as a source of inspiration. Although there are many aspects of the brain yet to be discovered, neuroscience has found evidence that the connections between neurons continuously grow and reshape as a part of the learning process. This differs from the design of Artificial Neural Networks, that achieve learning by evolving the weights in the synapses between them and their topology stays unaltered through time. This project has explored rules for growing the connections between the neurons in Spiking Neural Networks as a learning mechanism. These rules have been implemented on a multi-agent system for creating simple logic functions, that establish a base for building up more complex systems and architectures. Results in a simulation environment showed that for a given set of parameters it is possible to reach topologies that reproduce the tested functions. This project also opens the door to the usage of techniques like genetic algorithms for obtaining the best suited values for the model parameters, and hence creating neural networks that can adapt to different functions.