Mandelbrot Set

A high-performance C++ project exploring different approaches for calculating and rendering the Mandelbrot set, from vectorized SIMD implementations to arbitrary-precision arithmetic.

Features

• Generic Template Class: Supports rendering and processing the Mandelbrot set with customizable viewports, resolutions, and iteration depths using any arithmetic type.
• Vectorized Implementation: Utilizes FMA and AVX-256 instructions for high-speed calculations (optimized for single-precision floats).
• Multithreading: Built-in support for parallel execution using OpenMP.
• Deep Zoom Support: Includes an executable leveraging the Boost.Multiprecision library to render viewports at extreme zoom levels.
• PPM Image Library: A lightweight internal library for processing and saving images in the .ppm format.
• Custom Shaders: Includes two stylized color schemes: Indigo and Grey.

Prerequisites

Before building, ensure you have the following installed:

• GNU Multiprecision Library (GMP)
• Boost Library (specifically Multiprecision)
• OpenMP
• Hardware Support: The CPU must support AVX256 and FMA instructions for the vectorized implementation.

Installation

1. Clone the project:

   git clone https://github.com/yourusername/Mandelbrot-set
   cd Mandelbrot-set

2. Build the project:

   mkdir build && cd build
   cmake ..
   cmake --build .

Examples

Mandelbrot set rendered with the Grey shader:

Mandelbrot set rendered using the vectorized implementation:

Deep Zoom Example:

Center: (-1.295..., 0.440...) | Viewport: Square with side 5.1E-55.

Performance

The following measurements represent the time taken to render a single 4K frame on supported hardware:

Implementation	Rendering Time (Seconds)
Naive Implementation	0.752 s
Vectorized (AVX/FMA)	0.087 s