High-performance tool for generating stunning 1080p videos zooming deep into the Mandelbrot set with psychedelic color cycling.
Features Numba JIT compilation for near-C performance, supersampling anti-aliasing, and configurable zoom targets including the famous "Seahorse Valley" region.
- High Performance: Numba JIT compilation + NumPy vectorization for fast rendering
- Visual Quality: 1920×1080 resolution with 2x supersampling anti-aliasing
- Deep Zoom: Exponential zoom from 4.0 to 1e-5 width (100,000× magnification)
- Psychedelic Colors: Dynamic color cycling through customizable palettes
- Flexible Targets: Configurable zoom centers (defaults to Seahorse Valley mini-Mandelbrot)
- Progress Tracking: Real-time rendering progress with ETA
- FFmpeg Integration: High-quality H.264 encoding with web-optimized output
# Clone the repository
git clone https://github.com/nycarb/MandelbrotRender.git
cd MandelbrotRender
# Create virtual environment (recommended)
python3 -m venv .venv
source .venv/bin/activate # On Windows: .venv\Scripts\activate
# Install dependencies
pip install -r requirements.txtRequirements:
- Python 3.9+
- FFmpeg (for video encoding)
Install FFmpeg:
# macOS
brew install ffmpeg
# Ubuntu/Debian
sudo apt install ffmpeg
# Windows
# Download from https://ffmpeg.org/download.html# Generate full 60-second video (1800 frames, ~2-5 min render time)
python main.py
# Quick 5-second preview (150 frames, ~10-30 sec render time)
python main.py --preview
# Custom zoom location (Misiurewicz point)
python main.py --center-real -0.77568377 --center-imag 0.13646737 --duration 30Output video saved to: ./output/videos/mandelbrot_zoom.mp4
| Parameter | Value | Description |
|---|---|---|
| Resolution | 1920×1080 | Full HD output |
| Duration | 60 seconds | At 30 FPS = 1800 frames |
| Zoom Range | 4.0 → 1e-5 | 100,000× magnification |
| Target | Seahorse Valley | (-1.7497591, 0.0000001) |
| Iterations | 1000 base | Adaptive scaling with zoom depth |
| Supersampling | 2× | Anti-aliasing for smooth edges |
| Palette | psychedelic_rainbow | RGB color cycling |
The generator produces smooth zoom videos revealing the infinite self-similar detail of the Mandelbrot set:
- Wide view (0-10s) → Classic Mandelbrot bulb shape
- First zoom (10-25s) → Tendrils and spiral arms emerge
- Deep zoom (25-45s) → Self-similar mini-Mandelbrot copies appear
- Ultra-deep (45-60s) → Seahorse valley spirals and fractal complexity
Each frame cycles through psychedelic rainbow colors for hypnotic visual effect.
10 snapshot images are automatically saved during rendering to ./output/snapshots/ for trajectory verification.
- Numba JIT: Near C-speed computation of Mandelbrot iterations
- Parallel Processing: Multi-core CPU utilization via Numba's prange
- Vectorized: NumPy arrays for efficient pixel operations
- Memory-optimized: Processes frames individually to avoid RAM limits
- Adaptive Iterations: Dynamically scales max_iter based on zoom depth
Typical render times (Apple M2, 8 cores):
- Preview (150 frames): ~15 seconds
- Full video (1800 frames): ~3 minutes
# Fast 5-second preview
python main.py --preview# Seahorse Valley (default - spectacular mini-Mandelbrot)
python main.py --center-real -1.7497591 --center-imag 0.0000001
# Misiurewicz point (intricate spirals)
python main.py --center-real -0.77568377 --center-imag 0.13646737
# Feigenbaum point (period-doubling region)
python main.py --center-real -1.401155 --center-imag 0.0# Shorter 30-second video
python main.py --duration 30
# 60 FPS high framerate
python main.py --fps 60 --duration 30
# Higher quality with more iterations
python main.py --max-iter 2000 --supersample 4# Electric plasma palette
python main.py --palette electric_plasma
# Deep ocean blues
python main.py --palette deep_ocean
# Fire and ice
python main.py --palette fire_ice
# Available: psychedelic_rainbow, electric_plasma, deep_ocean,
# fire_ice, neon_dreams, sunset_glow# Extreme deep zoom (WARNING: 10^15 magnification, needs high max-iter)
python main.py --final-width 1e-15 --max-iter 5000 --duration 90
# Save individual frames as PNG
python main.py --save-frames
# Custom resolution (4K)
python main.py --width 3840 --height 2160 --supersample 1MandelbrotRender/
├── main.py # Entry point with CLI
├── requirements.txt # Python dependencies
├── mandelbrot_zoom/
│ ├── core/ # Mandelbrot computation engine
│ │ └── mandelbrot.py # Numba JIT-compiled iteration kernel
│ ├── rendering/ # Frame rendering pipeline
│ │ └── frame_renderer.py # Anti-aliasing & zoom scheduling
│ ├── color/ # Color palette system
│ │ └── palette.py # Cosine gradient color mapping
│ └── video/ # Video assembly
│ └── assembler.py # FFmpeg integration
└── output/
├── videos/ # Output MP4 files
├── snapshots/ # Sample PNG frames
└── frames/ # Individual frames (if --save-frames)
Uses the smooth iteration count algorithm for continuous gradients:
smooth_iter = n + 1 - log(log(|z|)) / log(2)
This eliminates banding artifacts and produces fluid color transitions.
Zoom width follows exponential decay for perceptually constant zoom speed:
log_widths = np.linspace(log(initial), log(final), num_frames)
widths = np.exp(log_widths)Deeper zooms reveal finer detail requiring more iterations:
zoom_factor = 4.0 / current_width
extra_iter = int(100 * log10(zoom_factor + 1))
max_iter = min(base_max_iter + extra_iter, 10000)Colors generated procedurally using Inigo Quilez's cosine gradient technique:
color(t) = a + b * cos(2π(c*t + d))
Allows smooth color cycling and psychedelic effects.
python main.py --helpMain options:
--preview: Quick 5-second preview--center-real,--center-imag: Zoom target coordinates--duration: Video length in seconds--fps: Frames per second (default: 30)--width,--height: Resolution (default: 1920×1080)--initial-width,--final-width: Zoom range--max-iter: Base iteration count (default: 1000)--supersample: Anti-aliasing factor (default: 2)--palette: Color scheme (default: psychedelic_rainbow)--save-frames: Save individual PNG frames
numpy>=1.24.0 # Vectorized computation
numba>=0.58.0 # JIT compilation for 10-100× speedup
pillow>=10.0.0 # Image processing
tqdm>=4.65.0 # Progress bars
torch>=2.0.0 # Tensor operations (used by palette system)
| Location | Coordinates | Description |
|---|---|---|
| Seahorse Valley | (-1.7497591, 0.0000001) | Classic mini-Mandelbrot spiral |
| Misiurewicz Point | (-0.77568377, 0.13646737) | Intricate spiral patterns |
| Feigenbaum Point | (-1.401155, 0.0) | Period-doubling cascade |
| Elephant Valley | (0.2549, 0.0005) | Elephant-trunk structures |
| Double Spiral | (-0.7269, 0.1889) | Dual spiral formation |
MIT License - see LICENSE file for details.
- Smooth coloring algorithm: Wikipedia - Mandelbrot Set
- Cosine palette technique: Inigo Quilez
- Numba project for JIT compilation capabilities
Contributions welcome! Feel free to open issues or submit pull requests.