THE MYCOFLUIDIC PROCESSOR: A Mathematical and Architectural Blueprint for Non-Electronic Biological-Fluidic Computation

Abstract

We present a comprehensive theoretical framework for the Mycofluidic Processor (MFP), a novel non-electronic computational paradigm integrating mycelial growth patterns with fluidic dynamics and pneumaticcontrol. The MFP architecture is based on a hexagonal honeycomb structure in which mycelial growth ismodulated by auxin signaling and pneumatic feedback. We detail the mathematical formalism governing theMFP’s behavior, including the coupling of 3D Cartesian-expanded Navier-Stokes momentum equations withreaction-diffusion auxin kinetics, the complete Jacobian stability analysis at the steady-state hyphal growththreshold, and the Biot poroelastic stress-strain tensor derivation for living mycelial matrix walls underpneumatic pressure gradients. Error propagation analysis covers structural collapse limits, wall shear stressversus hyphal adhesion thresholds, and pressure-relief mechanics. We conclude with a candid assessment ofthe MFP’s current limitations—including the temporal bottleneck between biological growth and computationalspeed—and chart future research horizons toward viable hybrid bio-electronic systems.