Since 1952, Turing instability has had one non-negotiable requirement: the inhibitor must diffuse faster than the activator. Fast inhibition, slow activation. This is the rule. Break it and patterns don't form.
Add superdiffusion — fractional Laplacian operators that model long-range transport — and the rule breaks. Instabilities can now occur when the activator diffuses faster than the inhibitor. The classical condition doesn't just bend. It reverses.
The mechanism is the combined effect of anomalous scaling exponents, diffusion rates, and domain size. Superdiffusion creates new instability windows that have no classical counterpart. The parameter space that was provably stable under normal diffusion becomes unstable under fractional transport. And the instabilities that emerge aren't gentle — superdiffusion promotes subcritical, explosive pattern formation rather than the gradual onset the classical theory predicts.
The lesson is about the scope of foundational results. Turing's condition wasn't wrong — it was derived under assumptions about transport that seemed universal but aren't. The 73-year-old rule was always contingent on a specific kind of spatial coupling. Change the coupling, and you change what's possible.
Every foundational constraint in physics has this structure: it's a theorem about a specific class of systems that gets taught as a law about all systems. The constraint is real. The universality is assumed.