Pic Breeder Imaginary

An evolutionary art tool that breeds complex number expressions as images. Inspired by Picbreeder.

Each image is generated by evaluating a mathematical expression over the complex plane, where each pixel coordinate z = x + yi is transformed through the expression, and the result is mapped to a color.

Screenshots

Main Selection Grid	Edit Mode

Examples

Generation 25	Generation 20

Features

• Complex Expression Evolution: Expressions include arithmetic (+, -, *, /, ^), transcendental functions (sin, cos, exp, log, sinh, cosh, tanh, sqrt), and special operations (conj, |z|, arg, Re, Im, max, min)
• Custom Transforms: spiral and wave functions for artistic patterns
• Loop Operation: A higher-order loop(n, body) that iterates body expression with continuous interpolation, creating fractal-like self-similar structures
• Multiple Color Modes: wheel, coords, vibrant, rainbow, fire, ice, twilight
• Complexity Control: Choose mutation bias (Decrease, Maintain, Slow+, Fast+) to guide expression growth
• Hybridization: Expressions you explore in edit mode are saved to a "trophy list" and can be combined with new expressions during evolution
• Interactive Evolution: Select your favorite from 12 variants to breed the next generation
• Edit Mode: Fine-tune constants in expressions using sliders with adjustable precision
• Undo Support: Go back to previous generations to explore different evolutionary paths
• High-Quality Export: Save individual images at 800x800 resolution

Building

Requires OCaml 4.14+, Dune, and SDL2.

# Install dependencies
opam install dune bogue tsdl

# Build
dune build

# Run
dune exec pic_breeder

Usage

Main Window

The main window displays a 4x3 grid of expression variants. Each cell shows a rendered image with a colored number indicator in the top-left corner.

Controls:

• Click on any image to select it as the parent for the next generation
• Ctrl+Click to enter edit mode for fine-tuning
• Undo - Revert to the previous generation
• Reset - Start fresh with new random expressions
• Regen - Generate new mutations from the current parent
• Color - Cycle through color modes (wheel, coords, vibrant, rainbow, fire, ice, twilight)
• Complexity - Cycle mutation bias (Decrease, Maintain, Slow+, Fast+)
• Trophies - View and manage the trophy list (click to remove)
• Ctrl+Z - Keyboard shortcut for undo
• Escape - Quit

The status bar shows the current generation number, color mode, complexity mode, and expression size statistics (min-max and average node count).

Edit Mode

Edit mode allows fine-tuning of an expression's constants using sliders. Each constant has separate sliders for its real and imaginary parts.

Controls:

• Sliders - Adjust constant values in real-time
• Zoom In/Out - Halve or double the slider range for finer or coarser control
• Save HQ - Export the image at 800x800 resolution
• Back - Return to the main grid

The expression text is displayed at the bottom, and the size info shows node count and number of constants.

Note: Entering edit mode adds the expression to the "trophy list" for hybridization - these expressions may be combined with future mutations.

Output

Images are saved to the output/ directory as PPM files. You can convert them using ImageMagick:

convert output/edited_gen_0010_pic_01.ppm output/image.png

How It Works

1. Expression Generation: Random expressions are generated as abstract syntax trees combining variables, constants, and operations
2. Mutation: Selected expressions undergo mutations including:
   • Wrapping nodes with unary operations
   • Inserting binary operations
   • Replacing subtrees with new random expressions
   • Perturbing constant values
   • Swapping operators
   • Hybridizing with trophy expressions (combining with previously-liked expressions)
3. Rendering: Each pixel (px, py) is mapped to a complex number z in the range [-2, 2] x [-2, 2], the expression is evaluated, and the result is converted to a color
4. Color Mapping: The complex result is mapped to color using various schemes (e.g., argument to hue, magnitude to brightness)

Project Structure

pic-breeder-imaginary/
├── lib/
│   ├── complex_expr.ml   # Complex number AST and evaluation
│   ├── mutation.ml       # Expression mutation and hybridization
│   ├── color.ml          # Complex-to-color mappings
│   ├── render.ml         # Image rendering
│   └── pic_breeder.ml    # Library exports
├── bin/
│   └── main.ml           # GUI application (Bogue/SDL2)
├── examples/             # Sample generated images
└── output/               # Saved high-quality images

License

MIT