Neurons are biological examples of excitable media. In computational neuroscience, the electric activity of neurons traditionally is modeled by coupled nonlinear differential equations, representing the dynamics of the membrane potential and variables related to the ionic conductances present in the system. A recent trend consists of the extension of this modeling strategy, detailing the neuronal dendritic trees through a compartmental approach. This detailed modeling aims at examining the possibility that these extensive tree-shaped neuronal regions play important functions, that is, they may be the stage for a complex “dendritic computation”. We propose a cellular automaton model of an active dendritic tree whose dynamics of signal transmission is simple, but whose topology is more faithfully reproduced by means of a Cayley tree with a large number of compartments. We study how the geometry of such an extended excitable system is able to perform computations on incoming stimuli. By both numerical and analytical means, we show that the model implements essential dendritic computations, such as signal compression (with dynamic ranges of more than 50 dB) and spike backpropagation. We also compare different tree like topologies for possible artificial stimulus detector applications. Finally, we discuss properties of other complex networks present in central nervous system.