Lévy Construction of Brownian Motion on [0,1] — Dyadic Refinement
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Level n (dyadic grid size = 2^n)
Current n:
6
Seed (deterministic RNG)
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B(1)
—
Max |B(t)|
—
Lévy midpoint rule: B(m)=½(B(a)+B(b))+2^{-(n+1)/2}Z. Interpolated linearly between dyadics.
Finance hook: to get a GBM path, set S_t=S_0·exp((r−½σ²)t+σB_t). (Not plotted here; you can add it easily.)