Six Exceptional Properties of the "Perez Hourglass": Perspectives toward New Types of Artificial Intelligence and Quantum Computers

Abstract
More than thirty-five years after the first intuitions linking self-organization, neuronal networks and the golden ratio (Perez, 1988), a remarkable numerical structure has finally emerged from the depths of Pascal’s triangle: the “Perez Hourglass”. This fractal, self-similar pattern, simultaneously antimatter of the famous Pascal triangle and digital incarnation of the Fibonacci sequence (OEIS A000975), reveals a perfect hourglass-shaped distribution of parity across the rows of the binomial triangle when analyzed through a specific recursive filtering method. Here we demonstrate for the first time that this structure is not merely a mathematical curiosity but constitutes an ideal topological substrate for a radically new generation of quantum computers: fractal quantum computers based on the Hourglass attractor.