The Developmental Péclet Number: Turing Reaction-Diffusion as Drift-Diffusion, Cell Fate as Void Crossing, and the Waddington Landscape as Void Geometry
Abstract
Turing's 1952 reaction-diffusion equations are drift-diffusion equations with spatial structure: the activator-inhibitor competition is governed by a Péclet number Pe_dev = D_activator/D_inhibitor, and pattern formation occurs precisely when Pe_dev > 1. The Waddington epigenetic landscape maps exactly onto void geometry — cell fate decisions are V* threshold crossings, differentiation is irreversible commitment above threshold, and cancer dedifferentiation is a conjugacy violation attempt. This paper derives the developmental Péclet number, maps morphogenesis milestones to Pe transitions, applies T3 (constraint cost), T10 (coupling floor for minimum morphogen concentration), and the Fantasia Bound (maximum potency × maximum commitment is impossible), and generates six falsifiable predictions extending the cross-substrate convergence of the void framework to developmental biology.
Fields of Study & Subjects
Developmental Biology and Gene Regulation
Nonlinear Dynamics and Pattern Formation
Gene Regulatory Network Analysis
Publication details
- Journal / source
- Zenodo (CERN European Organization for Nuclear Research)
- Publication date
- 26 February 2026
- Language
- EN
- Document type
- Preprint