# ============================================================ # Mandelbrot zoom — Google Colab (one-cell version) # ============================================================ # Paste into a fresh Colab cell and run. # Output: mandelbrot_zoom.mp4 + inline preview + download link. # ============================================================ import math, time, subprocess as sp, os, shutil, sys, importlib from pathlib import Path # ---- 1. Dependencies --------------------------------------- for pkg in ('numba', 'numpy', 'matplotlib', 'tqdm'): if importlib.util.find_spec(pkg) is None: sp.check_call([sys.executable, '-m', 'pip', 'install', '-q', pkg]) if shutil.which('ffmpeg') is None: sp.check_call([sys.executable, '-m', 'pip', 'install', '-q', 'imageio-ffmpeg']) import imageio_ffmpeg FFMPEG_BIN = imageio_ffmpeg.get_ffmpeg_exe() else: FFMPEG_BIN = shutil.which('ffmpeg') import numpy as np import numba as nb import matplotlib.pyplot as plt from tqdm.auto import tqdm from IPython.display import Video, FileLink, display print('numba', nb.__version__, '| numpy', np.__version__) print('ffmpeg ->', FFMPEG_BIN) # ---- 2. Parameters (edit me) ------------------------------- WIDTH = 1280 HEIGHT = 720 FPS = 30 N_FRAMES = 150 # 5 s @ 30 fps CENTER_X = -0.7436438870371587 # Seahorse Valley CENTER_Y = 0.13182590420531197 ZOOM_START = 1.0 ZOOM_END = 1e-4 # 10 000x zoom-in CRF = 20 PRESET = 'fast' OUTPUT_FILE = 'mandelbrot_zoom.mp4' print(f'Plan: {N_FRAMES} frames @ {WIDTH}x{HEIGHT}, {FPS} fps ' f'-> {N_FRAMES / FPS:.1f} s of video, zoom {ZOOM_START}->{ZOOM_END}') # ---- 3. Palette LUT (IQ cosine, precomputed) --------------- PALETTE_SIZE = 1024 def build_palette(n): t = np.linspace(0.0, 1.0, n, dtype=np.float64) ** 0.4 two_pi = 2.0 * math.pi r = 0.5 + 0.5 * np.cos(two_pi * (t + 0.00)) g = 0.5 + 0.5 * np.cos(two_pi * (t + 0.33)) b = 0.5 + 0.5 * np.cos(two_pi * (t + 0.67)) pal = np.empty((n, 3), dtype=np.uint8) pal[:, 0] = np.clip(r * 255.0, 0, 255).astype(np.uint8) pal[:, 1] = np.clip(g * 255.0, 0, 255).astype(np.uint8) pal[:, 2] = np.clip(b * 255.0, 0, 255).astype(np.uint8) return pal PALETTE = build_palette(PALETTE_SIZE) # global, read-only in kernel # ---- 4. Mandelbrot kernel (Numba, parallel, LUT colors) ---- @nb.njit(parallel=True, fastmath=True, cache=True) def mandelbrot_kernel(width, height, cx, cy, zoom, aspect, max_iter, palette): img = np.empty((height, width, 3), dtype=np.uint8) pal_n = palette.shape[0] inv_w = 1.0 / width inv_h = 1.0 / height inv_max = 1.0 / float(max_iter) for j in nb.prange(height): v_uv_y = 2.0 * (j + 0.5) * inv_h - 1.0 for i in range(width): u_uv_x = 2.0 * (i + 0.5) * inv_w - 1.0 px = (u_uv_x * aspect) * zoom + cx py = v_uv_y * zoom + cy zx = 0.0; zy = 0.0 zx2 = 0.0; zy2 = 0.0 k = 0 while k < max_iter and (zx2 + zy2) <= 4.0: zy = 2.0 * zx * zy + py zx = zx2 - zy2 + px zx2 = zx * zx zy2 = zy * zy k += 1 if k == max_iter: img[j, i, 0] = 13 img[j, i, 1] = 0 img[j, i, 2] = 26 else: # map k/max_iter -> LUT index (palette already has t**0.4 baked in) idx = int((k * inv_max) * (pal_n - 1)) if idx < 0: idx = 0 elif idx >= pal_n: idx = pal_n - 1 img[j, i, 0] = palette[idx, 0] img[j, i, 1] = palette[idx, 1] img[j, i, 2] = palette[idx, 2] return img def dynamic_max_iter(zoom, cx, cy): log_scale = math.log2(max(1.0 / max(zoom, 1e-6), 1.0)) pos_term = 0.5 * math.hypot(cx + 0.75, cy) mi = int(64.0 + 32.0 * min(max(log_scale + pos_term, 0.0), 12.0)) return min(mi, 512) def render_frame(zoom): aspect = WIDTH / HEIGHT mi = dynamic_max_iter(zoom, CENTER_X, CENTER_Y) return mandelbrot_kernel(WIDTH, HEIGHT, CENTER_X, CENTER_Y, zoom, aspect, mi, PALETTE) # ---- 5. JIT warmup + preview start frame -------------------- t0 = time.perf_counter() _ = mandelbrot_kernel(64, 32, -0.75, 0.0, 1.0, 2.0, 64, PALETTE) print(f'JIT compiled in {time.perf_counter()-t0:.1f} s') frame0 = render_frame(ZOOM_START) plt.figure(figsize=(10, 5.625)) plt.imshow(frame0) plt.axis('off') plt.title(f'Start frame zoom={ZOOM_START} ' f'maxIter={dynamic_max_iter(ZOOM_START, CENTER_X, CENTER_Y)}') plt.show() # ---- 6. Render & encode MP4 -------------------------------- cmd = [ FFMPEG_BIN, '-y', '-f', 'rawvideo', '-pixel_format', 'rgb24', '-video_size', f'{WIDTH}x{HEIGHT}', '-framerate', str(FPS), '-i', '-', '-c:v', 'libx264', '-preset', PRESET, '-crf', str(CRF), '-pix_fmt', 'yuv420p', '-movflags', '+faststart', OUTPUT_FILE, ] # stderr -> file to avoid the classic two-pipe deadlock ffmpeg_log = open('ffmpeg.log', 'wb') proc = sp.Popen(cmd, stdin=sp.PIPE, stderr=ffmpeg_log) log_start, log_end = math.log(ZOOM_START), math.log(ZOOM_END) t_render_start = time.perf_counter() for i in tqdm(range(N_FRAMES), unit='frame', desc='render'): t = i / max(N_FRAMES - 1, 1) zoom = math.exp(log_start + t * (log_end - log_start)) proc.stdin.write(render_frame(zoom).tobytes()) proc.stdin.close() proc.wait() ffmpeg_log.close() t_total = time.perf_counter() - t_render_start size_kb = os.path.getsize(OUTPUT_FILE) / 1024 print(f'\nDone in {t_total:.1f} s ({N_FRAMES / t_total:.1f} fps avg, ' f'{size_kb:.0f} KB) -> {OUTPUT_FILE}') if proc.returncode != 0: with open('ffmpeg.log', 'rb') as f: print('FFmpeg stderr (tail):\n', f.read()[-1500:].decode(errors='ignore')) # ---- 7. Preview & download -------------------------------- display(Video(OUTPUT_FILE, html_attributes='controls loop', embed=False, width=720)) display(FileLink(OUTPUT_FILE, result_html_prefix='Download: ')) # ---- 8. Bonus: single still at arbitrary zoom ------------- still_zoom = 1e-3 still = render_frame(still_zoom) plt.figure(figsize=(10, 5.625)) plt.imshow(still) plt.axis('off') plt.title(f'zoom={still_zoom} ' f'maxIter={dynamic_max_iter(still_zoom, CENTER_X, CENTER_Y)}') plt.show()