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Fractal Music Generator

Generate unique melodies based on Mandelbrot set fractal patterns.

GitHub: gddickinson/fractal_music_generator

Overview

A creative music generation system that translates mathematical patterns from the Mandelbrot set into musical compositions. Each unique coordinate in the fractal space generates a distinct melody, creating an infinite palette of algorithmic music.

Features

Fractal-to-Music Mapping

  • Mandelbrot Set Calculation: High-precision fractal generation
  • Pattern Recognition: Extract musical patterns from fractal iterations
  • Coordinate-Based Generation: Each point produces unique music
  • Infinite Variations: Unlimited unique melodies from fractal space

Musical Output

  • Melodic Generation: Convert fractal patterns to notes
  • Rhythmic Patterns: Derive timing from iteration counts
  • Harmonic Structure: Map fractal features to musical harmony
  • Audio Synthesis: Generate playable audio files

Customization

  • Zoom Levels: Explore different fractal scales
  • Coordinate Selection: Choose specific fractal regions
  • Musical Parameters: Adjust scales, tempo, instruments
  • Export Options: Save as MIDI or audio files

Installation

# Clone repository
git clone https://github.com/gddickinson/fractal_music_generator.git
cd fractal_music_generator

# Install dependencies
pip install numpy matplotlib scipy midiutil

# Run the generator
python fractal_music.py

Usage

Basic Generation

from fractal_music_generator import FractalMusicGenerator

# Create generator
generator = FractalMusicGenerator()

# Generate melody from coordinates
melody = generator.generate_from_coordinates(
    x=-0.7, 
    y=0.27015,
    zoom=1.0
)

# Export to MIDI
generator.export_midi(melody, "fractal_melody.mid")

Advanced Options

# Configure musical parameters
generator = FractalMusicGenerator(
    scale='major',           # Musical scale
    tempo=120,              # Beats per minute
    octave_range=(3, 6),    # Note range
    max_iterations=100      # Fractal precision
)

# Generate with custom parameters
melody = generator.generate(
    center_x=-0.5,
    center_y=0.0,
    zoom_level=2.0,
    resolution=128
)

How It Works

Fractal Calculation

  1. Generate Mandelbrot set for specified coordinates
  2. Calculate iteration counts for each point
  3. Extract pattern sequences from iteration data
  4. Map patterns to musical parameters

Music Mapping Algorithm

  1. Pitch: Iteration count modulo scale length
  2. Duration: Normalized iteration values
  3. Velocity: Gradient between adjacent points
  4. Timing: Sequential processing of fractal coordinates

Parameters

Parameter Description Default
x, y Fractal coordinates (-0.7, 0.27015)
zoom Magnification level 1.0
scale Musical scale (major, minor, pentatonic, etc.) 'major'
tempo BPM 120
max_iterations Fractal calculation depth 100
resolution Grid size for calculation 64

Musical Scales Supported

  • Major
  • Minor (Natural, Harmonic, Melodic)
  • Pentatonic
  • Blues
  • Chromatic
  • Whole Tone
  • Custom scales

Example Coordinates

Interesting fractal regions for music generation:

# Classic Mandelbrot antenna
x=-0.75, y=0.1

# Seahorse valley
x=-0.7, y=0.27015

# Elephant valley
x=0.3, y=0.03

# Triple spiral
x=-0.7269, y=0.1889

Output Formats

  • MIDI: For further editing in DAW
  • WAV: Direct audio output
  • Visualization: Fractal pattern plots
  • Musical Notation: Score generation (optional)

Technical Stack

Libraries

  • NumPy: Fractal calculations
  • SciPy: Audio processing
  • Matplotlib: Visualization
  • MIDIUtil: MIDI file generation
  • PyAudio (optional): Real-time playback

Applications

  • Generative Music: Algorithmic composition
  • Ambient Soundscapes: Evolving musical textures
  • Educational Tool: Visualize mathematics through sound
  • Sound Design: Unique audio material for production
  • Art Installations: Interactive fractal music exhibits

Future Enhancements

  • Real-time audio generation
  • 3D fractal exploration
  • Additional fractal types (Julia sets, Burning Ship, etc.)
  • Polyphonic harmony generation
  • Interactive GUI with visual feedback
  • Integration with music software via OSC/MIDI

Mathematical beauty transformed into musical patterns