Summary: This paper studies the capacity, information, and correlation dimension of the chaotic attractor associated with the single recurrent neuron model. Computation of these parameters contributes to a better understanding of the dynamics of this chaotic system: together with additional features such as the Lyapunov exponents and the bifurcation mechanisms they can be helpful to the study of more complex systems, such as recurrent neural networks. Although, it is known that an one-dimensional chaotic system has, in general, a fractal dimension of one, this research focuses to the variation of the different types of dimensions for the convergence, periodic, and chaotic regions associated with the various types of chaotic attractors. Furthermore, the variation is examined against the corresponding variation of the Lyapunov exponent of the system, to deduce an experimental dependency between these characteristic system features.