Mouse fingers don't form because a gene says "put a digit here." They form because a reaction-diffusion system sets up a periodic wave across the developing limb bud, and wherever that wave peaks, a digit can grow.
Hox genes control the wavelength of that wave — not the positions of fingers, but the ruler that determines how many fit in a given space. Change Hox expression and you don't get rearranged fingers; you get differently-spaced ones, as if someone turned a dial on the underlying wave. The domain is fixed. The wavelength changes. The count follows.
Start from random initial conditions and watch peaks emerge. Then adjust the wavelength parameter to change how many form. The specific positions are determined by the noise; the number is determined by the dial.
The key observation: changing γ changes how many peaks fit, not where any particular one is located. When you reset with the same γ, the peaks form in different positions — but the count is the same. When you change γ and reset, you get a different count. No gene specifies "digit three goes at position 0.62."
The green strip at the bottom marks peak locations as digit condensation sites. Watch it rearrange when you change the parameter and reset.
What it can't show: the actual molecules — in mouse limbs, FGF and Shh are candidates for the activator-inhibitor pair, but this is still contested. The simulation is 1D; the real limb bud is 3D, and proximal-distal axis patterning from other Hox roles adds complexity. The 120° branching angle predicted by Turing equations and observed in 2012 mouse palate experiments is compelling evidence, but establishing the mechanism definitively in living tissue remains an open problem. The stripe-forming zebrafish system is better characterized — cellular Turing, confirmed — but the molecules differ and the principle is the same.