Add percolation phase-transition demo at /percolation

[ianalloway]

Summary

• Adds /percolation — an interactive site-percolation lattice where a phase transition is directly visible
• src/features/percolation/perc.ts: fixed per-site noise field thresholded at p (so the slider grows/shrinks one configuration continuously), flat-array BFS cluster labeling, spanning-cluster detection, fill and largest-cluster stats
• src/pages/Percolation.tsx: canvas lattice with the spanning cluster in bright green, p slider with live distance-to-p_c readout, auto-sweep through the critical region, new-field reroll
• src/App.tsx: lazy-loaded /percolation route with SEO metadata

How it works

• Each site holds a fixed uniform random value; it's open iff that value < p — so dragging the slider adds/removes sites monotonically instead of resampling, which makes the transition legible
• BFS labels connected clusters; a cluster touching both top and bottom rows is the spanning cluster and renders bright green
• Below p_c ≈ 0.5927 there's (almost) never a spanning cluster; above it, (almost) always — near p_c it flickers into existence and the largest-cluster share jumps, the classic second-order phase transition
• Auto-sweep ping-pongs p between 0.35 and 0.75 to replay the transition; the p_c readout turns yellow within ±0.02 of critical

Test plan

• Load /percolation — p=0.45, scattered dim clusters, "disconnected"
• Slide p up — at ~0.59 a bright green spanning cluster snaps in, header flips to "⚡ percolates"
• Slide back down — spanning cluster breaks apart around the same region
• Auto sweep — the transition replays each pass through p_c
• Largest-cluster % jumps sharply through the transition while fill % rises smoothly
• New field rerolls; the exact transition point shifts slightly (finite-size effects)
• Slider grows/shrinks the same pattern — sites don't rearrange
• Resize builds a fresh lattice fitted to the window

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Generated by Claude Code

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