Is continued fraction a representational basis for neuronal computing?

The author examines the question of whether the continued fraction (CF) is a representational basis for neuronal computing. It is argued that when real or complex numbers are represented by physical quantities such as voltage, current, impedance, etc. and handled using bio-hardware, a natural mathematical representation that supports algorithmic manipulation is the CF. Arguments are provided from network theory, neural network models and distributed algorithm design. In particular, a matrix inversion free linear time algorithm based on CF is described for temporal rational interpolation that can be used for the design of impulse response filters, in conjunction with Laplace or z-transforms.<>