""" Peano / Hilbert Curve Animation for @fminxyz Telegram Channel 1080x1080 px, 12 fps, 25 seconds (= 300 frames) Four acts: Act 1 (0-7s): Hilbert curve iterations 1 → 5 (progressive draw) Act 2 (7-14s): Level-6 curve filling the square (rainbow gradient) Act 3 (14-20s): Locality property demo Act 4 (20-25s): Applications text reveal """ import os import sys import tempfile import subprocess import numpy as np import matplotlib matplotlib.use('Agg') import matplotlib.pyplot as plt from matplotlib.collections import LineCollection import warnings warnings.filterwarnings('ignore') OUTPUT = "/root/Strategy/content/drafts/peano_curve_animation.mp4" FPS = 12 DUR = 25 NFRAM = FPS * DUR # 300 DPI = 100 FW, FH = 10.8, 10.8 BG = "#1a1a2e" PAN = "#16213e" CYAN = "#00d4ff" GREE = "#00ff99" PINK = "#ff6b9d" TXT = "#e8e8f0" ACC = "#a8a8ff" GRD = "#2a2a4a" YELL = "#ffe066" ORG = "#ff9933" # ── Hilbert curve generation (iterative, integer grid) ────────────────────── def hilbert_xy(n): """Return (x, y) arrays of Hilbert curve points for order n. Grid size = 2^n, so 4^n points total.""" N = 1 << n # 2^n total = N * N xs = np.zeros(total, dtype=float) ys = np.zeros(total, dtype=float) for i in range(total): x = y = 0 s = 1 t = i while s < N: rx = 1 if (t & 2) else 0 ry = 1 if (t & 1) ^ rx else 0 # rotate if ry == 0: if rx == 1: x = s - 1 - x y = s - 1 - y x, y = y, x x += s * rx y += s * ry t >>= 2 s <<= 1 xs[i] = x ys[i] = y # normalize to [0, 1] xs = xs / (N - 1) ys = ys / (N - 1) return xs, ys # Precompute curves for levels 1..6 print("Precomputing Hilbert curves ...") curves = {} for level in range(1, 7): curves[level] = hilbert_xy(level) print(f" level {level}: {len(curves[level][0])} points") # ── Frame timing ───────────────────────────────────────────────────────────── A1S, A1E = 0, 7 * FPS # 0..84 A2S, A2E = 7 * FPS, 14 * FPS # 84..168 A3S, A3E = 14 * FPS, 20 * FPS # 168..240 A4S, A4E = 20 * FPS, NFRAM # 240..300 BLEND = 4 def cl(v, lo=0.0, hi=1.0): return float(max(lo, min(hi, v))) def fp(local, s, e, dur): a = s * dur b = e * dur return cl((local - a) / max(1, b - a)) def ease(t): """Smooth ease in-out.""" return t * t * (3 - 2 * t) def sty_ax(ax): ax.set_facecolor(PAN) ax.set_xlim(-0.06, 1.06) ax.set_ylim(-0.06, 1.06) ax.set_aspect('equal') ax.tick_params(left=False, bottom=False, labelleft=False, labelbottom=False) for sp in ax.spines.values(): sp.set_color(GRD) sp.set_linewidth(1.2) # ── ACT 1: Hilbert iterations 1→5 ──────────────────────────────────────────── def act1(f, ax, axT, axB): lf = f - A1S dur = A1E - A1S # Show levels sequentially, each occupying ~1.2s (14 frames) # Levels 1-5 across the 7s window with overlap # Level k visible in [k-1, k+0.4] / 5 fraction level_times = { 1: (0.00, 0.20), 2: (0.18, 0.38), 3: (0.35, 0.56), 4: (0.53, 0.74), 5: (0.71, 1.00), } # Determine which level to show current_level = 1 for lv in [5, 4, 3, 2, 1]: ts, te = level_times[lv] if lf / dur >= ts: current_level = lv break ts, te = level_times[current_level] progress_in_level = fp(lf, ts, te, dur) draw_frac = ease(progress_in_level) xs, ys = curves[current_level] n_pts = len(xs) n_draw = max(2, int(draw_frac * n_pts)) # Draw curve up to n_draw ax.plot(xs[:n_draw], ys[:n_draw], color=CYAN, lw=max(0.5, 3.0 - 0.4 * current_level), alpha=0.92, solid_capstyle='round') # Level label ax.text(0.5, -0.04, f'Итерация {current_level} ({n_pts} точек)', ha='center', va='top', fontsize=14, color=ACC, transform=ax.transAxes) # Title fa0 = fp(lf, 0.00, 0.12, dur) axT.text(0.5, 0.55, 'Кривая Гильберта', ha='center', va='center', fontsize=30, fontweight='bold', color=TXT, alpha=fa0) axT.text(0.5, 0.10, 'Hilbert Curve', ha='center', va='center', fontsize=16, color=ACC, alpha=fa0 * 0.8) # ── ACT 2: Space-filling at level 6 ────────────────────────────────────────── def act2(f, ax, axT, axB): lf = f - A2S dur = A2E - A2S xs, ys = curves[6] n_pts = len(xs) draw_frac = ease(fp(lf, 0.00, 0.80, dur)) n_draw = max(2, int(draw_frac * n_pts)) # Segments with viridis colormap t_vals = np.linspace(0, 1, n_draw) segs = np.stack([np.c_[xs[:n_draw - 1], ys[:n_draw - 1]], np.c_[xs[1:n_draw], ys[1:n_draw]]], axis=1) lc = LineCollection(segs, cmap='plasma', norm=plt.Normalize(0, 1), linewidths=0.9, alpha=0.88) lc.set_array(t_vals[:-1]) ax.add_collection(lc) # Fill percentage text fill_pct = draw_frac * 100 fa_pct = fp(lf, 0.25, 0.50, dur) ax.text(0.5, -0.04, f'Заполнение: {fill_pct:.0f}%', ha='center', va='top', fontsize=14, color=GREE, transform=ax.transAxes, alpha=fa_pct) fa0 = fp(lf, 0.00, 0.12, dur) axT.text(0.5, 0.55, 'Заполнение квадрата', ha='center', va='center', fontsize=28, fontweight='bold', color=TXT, alpha=fa0) axT.text(0.5, 0.10, '4096 × 4096 = 16 млн точек', ha='center', va='center', fontsize=14, color=ACC, alpha=fa0 * 0.7) # Colorbar label fa_cb = fp(lf, 0.50, 0.80, dur) axB.text(0.5, 0.65, 'Цвет = позиция вдоль кривой', ha='center', va='center', fontsize=14, color=ACC, alpha=fa_cb) axB.text(0.5, 0.25, 'непрерывная биективная функция [0,1] → [0,1]²', ha='center', va='center', fontsize=12, color=YELL, alpha=fa_cb * 0.85) # ── ACT 3: Locality property ────────────────────────────────────────────────── def act3(f, ax, axT, axB): lf = f - A3S dur = A3E - A3S # Full level-5 curve as backdrop xs5, ys5 = curves[5] ax.plot(xs5, ys5, color='#334466', lw=1.2, alpha=0.5, zorder=1) # Two nearby points on the curve and their 2D proximity # Pick indices ~5% apart on level-5 curve n5 = len(xs5) idx_a = int(0.35 * n5) idx_b = int(0.40 * n5) # close on curve idx_c = int(0.80 * n5) # far on curve, far in space xa, ya = xs5[idx_a], ys5[idx_a] xb, yb = xs5[idx_b], ys5[idx_b] xc, yc = xs5[idx_c], ys5[idx_c] # Phase 1: show two close points f1 = fp(lf, 0.00, 0.28, dur) if f1 > 0.01: ax.scatter([xa, xb], [ya, yb], color=CYAN, s=120, zorder=5, alpha=f1) # Phase 2: draw arrow between them in 2D + text f2 = fp(lf, 0.22, 0.50, dur) if f2 > 0.01: ax.annotate('', xy=(xb, yb), xytext=(xa, ya), arrowprops=dict(arrowstyle='<->', color=CYAN, lw=2.0, alpha=f2)) dist2d = np.sqrt((xa - xb)**2 + (ya - yb)**2) mx, my = (xa + xb) / 2, (ya + yb) / 2 ax.text(mx + 0.04, my + 0.04, f'd₂D = {dist2d:.3f}', fontsize=11, color=CYAN, alpha=f2) # Phase 3: show position on 1D curve (highlight segment) f3 = fp(lf, 0.40, 0.65, dur) if f3 > 0.01: seg_len = idx_b - idx_a ax.plot(xs5[idx_a:idx_b], ys5[idx_a:idx_b], color=YELL, lw=3.5, alpha=f3 * 0.9, zorder=3) frac_1d = seg_len / n5 ax.text(0.5, -0.04, f'Близко на кривой: {frac_1d * 100:.1f}% пути', ha='center', va='top', fontsize=13, color=YELL, transform=ax.transAxes, alpha=f3) # Phase 4: locality text f4 = fp(lf, 0.60, 0.90, dur) if f4 > 0.01: ax.text(0.5, 0.5, 'Locality\nPreserving', ha='center', va='center', fontsize=22, fontweight='bold', color=GREE, alpha=f4 * 0.9, transform=ax.transAxes, bbox=dict(boxstyle='round,pad=0.5', facecolor='#001a0d', edgecolor=GREE, alpha=f4 * 0.7)) fa0 = fp(lf, 0.00, 0.14, dur) axT.text(0.5, 0.55, 'Свойство локальности', ha='center', va='center', fontsize=28, fontweight='bold', color=TXT, alpha=fa0) axT.text(0.5, 0.10, 'Близкие точки на кривой → близкие в 2D', ha='center', va='center', fontsize=14, color=CYAN, alpha=fa0) # ── ACT 4: Applications ─────────────────────────────────────────────────────── def act4(f, ax, axT, axB): lf = f - A4S dur = A4E - A4S # Faded curve in background xs5, ys5 = curves[5] ax.plot(xs5, ys5, color='#223355', lw=1.0, alpha=0.3, zorder=1) apps = [ (0.08, 0.42, "LSH\n(Locality-Sensitive Hashing)", CYAN, 0.10, 0.48), (0.30, 0.42, "Database indexing\n(Z-order / Morton)", GREE, 0.30, 0.65), (0.55, 0.42, "Neural architecture\n(ViT patch ordering)", ACC, 0.52, 0.82), (0.75, 0.42, "Google S2\ngeo-indexing", YELL, 0.72, 1.00), ] # Draw each app as floating box appearing sequentially for (ts, te, label, color, xs_pos, ys_pos) in apps: fa = fp(lf, ts, te, dur) if fa > 0.01: ax.text(xs_pos, ys_pos, label, ha='center', va='center', fontsize=13, fontweight='bold', color=color, alpha=fa, transform=ax.transAxes, bbox=dict(boxstyle='round,pad=0.5', facecolor=BG, edgecolor=color, linewidth=1.5, alpha=fa * 0.9)) # Connection lines from curve to boxes (appear with boxes) # Just a visual connector dot on the curve connector_pts = [ (int(0.15 * len(xs5)), CYAN), (int(0.35 * len(xs5)), GREE), (int(0.60 * len(xs5)), ACC), (int(0.80 * len(xs5)), YELL), ] for (ci, (ts, te, *_)), (idx, color) in zip( enumerate(apps), connector_pts): fa = fp(lf, ts, te, dur) if fa > 0.01: ax.scatter([xs5[idx]], [ys5[idx]], color=color, s=80, zorder=4, alpha=fa) fa0 = fp(lf, 0.00, 0.14, dur) axT.text(0.5, 0.55, 'Применения', ha='center', va='center', fontsize=32, fontweight='bold', color=TXT, alpha=fa0) axT.text(0.5, 0.10, 'Кривая Гильберта в современных системах', ha='center', va='center', fontsize=14, color=ACC, alpha=fa0 * 0.8) # ── Main render loop ────────────────────────────────────────────────────────── def make_frame(frame, fig, ax, axT, axB): fig.patch.set_facecolor(BG) ax.cla() axT.cla(); axT.axis('off') axB.cla(); axB.axis('off') axT.set_xlim(0, 1); axT.set_ylim(0, 1) axB.set_xlim(0, 1); axB.set_ylim(0, 1) sty_ax(ax) if frame < A1E - BLEND: act1(frame, ax, axT, axB) elif frame < A2S + BLEND: p = (frame - (A1E - BLEND)) / (2 * BLEND) if p < 0.5: act1(frame, ax, axT, axB) else: act2(frame, ax, axT, axB) elif frame < A2E - BLEND: act2(frame, ax, axT, axB) elif frame < A3S + BLEND: p = (frame - (A2E - BLEND)) / (2 * BLEND) if p < 0.5: act2(frame, ax, axT, axB) else: act3(frame, ax, axT, axB) elif frame < A3E - BLEND: act3(frame, ax, axT, axB) elif frame < A4S + BLEND: p = (frame - (A3E - BLEND)) / (2 * BLEND) if p < 0.5: act3(frame, ax, axT, axB) else: act4(frame, ax, axT, axB) else: act4(frame, ax, axT, axB) def main(): tmpdir = tempfile.mkdtemp(prefix='peano_') print(f"Rendering {NFRAM} frames ({DUR}s @ {FPS}fps) → {tmpdir}") fig = plt.figure(figsize=(FW, FH), dpi=DPI, facecolor=BG) ax = fig.add_axes([0.08, 0.14, 0.84, 0.70]) axT = fig.add_axes([0.0, 0.86, 1.0, 0.12], facecolor='none') axT.set_xlim(0, 1); axT.set_ylim(0, 1); axT.axis('off') axB = fig.add_axes([0.0, 0.00, 1.0, 0.13], facecolor='none') axB.set_xlim(0, 1); axB.set_ylim(0, 1); axB.axis('off') for i in range(NFRAM): make_frame(i, fig, ax, axT, axB) fig.savefig(os.path.join(tmpdir, f"f{i:04d}.png"), facecolor=BG, dpi=DPI) if i % 30 == 0: print(f" {i}/{NFRAM}", flush=True) plt.close(fig) print("Encoding with ffmpeg ...") cmd = ['ffmpeg', '-y', '-framerate', str(FPS), '-i', os.path.join(tmpdir, 'f%04d.png'), '-c:v', 'libx264', '-preset', 'fast', '-crf', '20', '-pix_fmt', 'yuv420p', '-movflags', '+faststart', OUTPUT] r = subprocess.run(cmd, capture_output=True, text=True) if r.returncode != 0: print("ffmpeg error:\n", r.stderr[-2000:]) sys.exit(1) import shutil; shutil.rmtree(tmpdir) size_mb = os.path.getsize(OUTPUT) / 1e6 print(f"Done! {OUTPUT} ({size_mb:.1f} MB)") # Verify with ffprobe probe = subprocess.run( ['ffprobe', '-v', 'quiet', '-print_format', 'json', '-show_streams', OUTPUT], capture_output=True, text=True) print("ffprobe output:", probe.stdout[:500]) if __name__ == '__main__': main()