Mandelbrot Renderer

A Mandelbrot set generator implemented in Rust, optimized for high-resolution output.

Algorithm Overview

Fractal Generation logic

The renderer generates the Mandelbrot set by iterating the complex quadratic polynomial: $z_{n+1} = {z_n}^2 + c$

For each pixel $(x, y)$ in the output image:

1. Coordinate Mapping: The pixel coordinates are mapped to a point $c$ in the complex plane ($c = a + bi$).
2. Iteration: Starting with $z_0 = 0$, the function is applied repeatedly.
3. Escape Condition: If the magnitude $|z|$ exceeds a threshold (256) within the maximum number of iterations, the point is considered to "escape" to infinity.
4. Coloring: The number of iterations taken to escape, combined with a renormalization factor, determines the pixel color. Points that do not escape are considered part of the Mandelbrot set.

Technical Implementation

• Memory Management: Images are rendered and written line-by-line to allow massive scale renders (e.g., 35,000px+) on systems with limited RAM.
• Optimizations: Geometric checks are used to skip interior points (Cardioid/Bulb), and binary P6 PPM output is used for fast I/O.

Dependencies

• rayon: Used for parallelizing the computation of each row across all CPU cores.

Execution

To run with full optimizations:

cargo run --release

LICENSE

• MIT