Fourier lab: 50,000-epicycle cap (FFT + scaled sampling), default speed 120 - #16
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… speed 120 The term count is bounded by the sample count (K ≤ M−1), so raising the cap alone would have done nothing. The lab now requests a power-of-two sample count that grows with the requested epicycles (2048 → 65536), and the rule takes a radix-2 FFT path for power-of-two inputs (O(M log M); the naive O(M²) DFT remains for other sizes, with an equivalence test). The trace step count is decoupled from the sample count (2000 steps), so a full trace still takes ~17 s at the new default speed of 120. The viz skips arms whose ring is sub-pixel — with 50k terms nearly all are — so per-frame geometry stays proportional to what's visible. Schema/input/URL cap: 2000 → 50,000. Test mocks of textPath keep its pure helpers real (partial mock). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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Raising the cap required real work underneath: K ≤ M−1, so the lab now samples the text at a power-of-two count that scales with the requested epicycles (2048–65536), and the rule uses a radix-2 FFT for power-of-two inputs (naive DFT kept for other sizes; equivalence test added). Trace steps are decoupled from sample count (2000) so a trace still takes ~17 s at the new default speed 120. The viz culls sub-pixel arms like it already culled sub-pixel rings. Tests: Rust +2, web +2.