🌀 Fract-ol

Explore the beauty of fractals — 42 Network project

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📖 About

Fract-ol is a 42 school project that renders beautiful mathematical fractals in real-time using the miniLibX graphics library. By implementing the Mandelbrot and Julia sets, you can zoom infinitely into stunning, self-similar patterns — all generated from simple mathematical formulas.

This project is an exploration of complex numbers, iterative algorithms, and computer graphics.

✨ Features

• 🎨 Mandelbrot Set — The iconic fractal with infinite zoom
• 🌈 Julia Set — Parametric fractal with customizable constants
• 🔍 Infinite Zoom — Scroll to zoom in/out with mouse cursor tracking
• 🖱️ Mouse Navigation — Zoom follows the cursor position
• ⌨️ Keyboard Controls — Arrow keys to pan the view
• 🎭 Color Palettes — Psychedelic color mapping based on iteration count

🚀 Getting Started

Prerequisites

• GCC compiler
• Make
• miniLibX (included or install via package manager)
• X11 libraries (sudo apt install libx11-dev libxext-dev on Ubuntu)
• A UNIX-based OS (Linux / macOS)

Build

git clone https://github.com/JMADIL/FRACT-OL.git
cd FRACT-OL
make

Usage

# Render the Mandelbrot set
./fractol mandelbrot

# Render a Julia set with custom parameters
./fractol julia <real> <imaginary>

Examples:

./fractol julia -0.766667 -0.090000    # Classic Julia spiral
./fractol julia 0.285 0.01             # Dendrite pattern
./fractol julia -0.4 0.6               # Lightning bolts

Controls

Input	Action
Scroll Up	Zoom in (follows cursor)
Scroll Down	Zoom out (follows cursor)
Arrow Keys	Pan the view
ESC	Exit

📂 Project Structure

FRACT-OL/
├── Makefile            # Build system
├── fractol.h           # Header with structs & prototypes
├── main.c              # Entry point & argument parsing
├── init_fract.c        # Fractal initialization & window setup
├── fractal_render.c    # Mandelbrot & Julia rendering algorithms
├── events.c            # Mouse & keyboard event handlers
└── utils/              # Utility functions

🏗️ How It Works

The Mandelbrot Set

For each pixel (x, y) on screen, map it to a complex number c = a + bi, then iterate:

z₀ = 0
zₙ₊₁ = zₙ² + c

If |zₙ| > 2 → pixel is OUTSIDE (color based on iteration count)
If iterations reach max → pixel is INSIDE (typically black)

The Julia Set

Similar to Mandelbrot, but c is a fixed constant and z₀ varies per pixel:

z₀ = pixel position
zₙ₊₁ = zₙ² + c    (c is constant, e.g., -0.766667 - 0.09i)

Color Mapping

Iteration count ──► Color value
     0          ──► Dark (deep inside the set)
     1-10       ──► Blues & purples
     10-50      ──► Greens & yellows
     50+        ──► Reds & whites (near the boundary)

🔑 Key Concepts Learned

Concept	Description
Complex Numbers	Working with real + imaginary components
Iterative Algorithms	Convergence/divergence testing per pixel
miniLibX	Pixel-level rendering and event handling
Color Theory	Mapping iteration depth to RGB color values
Coordinate Mapping	Screen pixels ↔ complex plane coordinates
Optimization	Efficient rendering for real-time interaction

👤 Author

Adil Jamoun — @JMADIL

🏫 1337 Coding School (42 Network) — Morocco