Creation of long-term mental representations using the dimension of fractal dendrites

This work explores the possibility of using a neuron's dendrite spatial dimension as primitives for creating representations of mental activity. Recent in-vivo experimental results show that: (a) spines are structurally unstable and (b) adult dendrites are not static. These results suggest that using the synapse alone to create mental representations is insufficient. Using diffusional type equations, as models for the voltage fluctuations at a neuron's soma due to massive synaptic activity, two experiments were performed: (a) the autocorrelation function of the cable equation with fractal boundary conditions was determined and compared to those of the Ornstein-Uhlenbeck and Tuckwell-Walsh random processes and (b) these autocorrelation functions remained unchanged in spite of drastic regression of its branches. These results hint at a remarkably stable possible form of "information" storage.