================================================================
(1) STEADY STATE
    u* = 1.000000   v* = 0.900000
    check f = a-u+u^2 v = 0.00e+00  (should be 0)
    check g = b  -u^2 v = 0.00e+00  (should be 0)
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(2) REACTION-ONLY STABILITY  (no diffusion)
    kinetics J = [[+0.8000, +1.0000], [-1.8000, -1.0000]]
    Tr(gamma J) = -2860.0000   (< 0 required)  -> STABLE
    Det(gamma J)= +204490000.0000  (> 0 required)  -> OK
    eigenvalues of gamma J: [-1430.+14228.32035062j -1430.-14228.32035062j]
    => with no diffusion every small perturbation decays. The uniform
       state is stable. (This is the surprise to come.)
================================================================
(3) DISPERSION RELATION  (with diffusion, d = 40.0)
    Turing cond (i)  d*fu+gv = +31.0000  (> 0 ?) -> True
    Turing cond (ii) (d*fu+gv)^2 - 4 d Det = +801.0000 (> 0 ?) -> True
    critical ratio d_c = 8.5676  (Turing needs d > d_c; here d=40.0)
    k_c^2 (min of det M) = 5541.250
    fastest-growing k* = 50.2894  (k*^2=2529.027), growth lambda* = 5877.460
    unstable band: k in [21.962, 102.957]
    PREDICTED pattern wavelength  L* = 2 pi / k* = 0.12494
    (domain is [0,1]^2, so expect ~ 8.00 wavelengths across)
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(4) 2D SIMULATION  -> measure emergent wavelength, compare to prediction
    (each run compares its OWN linear prediction to its OWN measurement;
     wavelength scales with gamma, so the absolute number differs by row)
  (4a) THE PAGE'S CONFIG (gamma=14300, d=40, 128^2), measured exactly as
       the browser does (row+col FFT, integer mode m -> wavelength 1/m):
       22000 steps · predicted 2pi/k* = 0.1249 (8.00 features) · measured = 1/8 = 0.1250 · amplitude 1.095
       k*=50.289; the cell holds ~8 features and 8 fits exactly, so the
       page shows a clean predicted=measured match (8 features).
  (4b) PREDICTED ONSET feature-count vs d on the page (linear k*); the
       saturated pattern tracks this within ~one feature (nonlinear
       selection settles a touch shorter -> +0..1 feature):
       d=  12: predicted onset wl 0.0969  ->  ~10 features
       d=  20: predicted onset wl 0.1080  ->  ~9 features
       d=  40: predicted onset wl 0.1249  ->  ~8 features
  (4c) CLEAN, quantization-free check (gamma=1000, d=40, large field L=8,
       ~17 wavelengths so no rounding; sub-bin radial peak):
       grid 238^2, 6029 steps · predicted 0.4725 · measured 0.4631 · err 2.0% · amplitude 1.072
================================================================
(5) CONTROL  d = 1 (equal diffusion): linear theory predicts NO pattern
    max growth rate over all k (d=1): -1430.0000  (<=0 => stable)
    simulated pattern amplitude (std of u): 4.76e-16  (~0 => flat)
================================================================
SUMMARY: a uniform state, provably stable without diffusion, is
destabilized BY diffusion into a pattern whose wavelength the linear
theory predicts. Turn the diffusion difference off and the pattern dies.