Harmonic fractal transformation for modeling complex neuronal effects: from bursting and noise shaping to waveform sensitivity and noise-induced subthreshold spiking

We propose the first fractal frequency mapping, which in a simple form enables to replicate complex neuronal effects. Unlike the conventional filters, which suppress or amplify the input spectral components according to the filter weights, the transformation excites novel components by a fractal recomposition of the input spectra resulting in a formation of spikes at resonant frequencies that are optimal for sampling. This enables high sensitivity detection, robustness to noise and noise-induced signal amplification. The proposed model illustrates that a neuronal functionality can be viewed as a linear summation of spectrum over nonlinearly transformed frequency domain.