README.md

Fractal Project

📜 About Project · 📑 Fractals List · 🎮 Controls · 👨‍💻 Usage · 🌄 Screenshots

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📜 About Project

A fractal is a fragmented geometrical figure that infinitely repeats at smaller scales.
So this project generates beautiful fractals from the complex numbers of an iterative mathematical construct.
For graphics, I used SFML library and NVIDIA CUDA Toolkit for parallel computing.
Project builds by CMake build system, so if you do not have CUDA Toolkit or your platform doesn't have CUDA support, CMake will build this project without CUDA support and computing will be done through CPU threads.
By default, there will be 40 parallel threads, the color is rgb(21, 0, 0) and the window size is 800px.

Note

If you want to change color, threads count, window size, or other defaults, change them in helpers.hpp file.

📑 Fractals List

The program supports these fractal sets:

Name	Formula
Mandelbrot	$z_{n+1} = z_n^2 + c, z_0 = 0$
Julia	$z_{n+1} = z_n^2 + c, z_0 = c$
Burning Ship	$z_{n+1} = abs(z_n^2) + c, z_0 = 0$
Tricorn	$z_{n+1} = \overline{z_n}^2 + c, z_0 = 0$
Mandelbox	It's more complex, see this article
Multibrot	$z_{n+1} = z_n^d + c, z_0 = 0, d = 5$
Mandelbar	Take a look at Mandelbar 5th (horizontal) in this image
Per. Burning Ship	Take a look at Perpendicular Burning Ship in this image
Celtic Mandelbrot	Take a look at Celtic Mandelbrot in this image

Useful Links:

https://www.deviantart.com/kosmic-stardust/art/Mandelbrot-ABS-Variations-Complete-Set-of-Formulas-487039852 https://www.deviantart.com/kosmic-stardust/art/4th-Order-ABS-Mandelbrot-Variations-Complete-Set-601300868 https://www.deviantart.com/kosmic-stardust/art/5th-Order-ABS-Mandelbrot-Variations-601484985

🎮 Controls

The program supports the following controls:

Key	Description
ESC	Close the program window
Keys [1-9]	Move to another fractal
Key R	Change the red component of fractal
Key G	Change the green component of fractal
Key B	Change the blue component of fractal
Mouse Scroll	Zoom in and out of the fractal
⬆️ ⬇️ ⬅️ ➡️	Change the viewpoint
Key L	Lock Julia's fractal
Zero	Reset the fractal to its initial state

👨‍💻 Usage

Requirements

The program is written in C++ and thus needs the g++ compiler and some standard C++ libraries to run.
Also needs to install SFML library and CMake. If you want to use your NVIDIA GPU power, you need to install NVIDIA CUDA Toolkit.

Instructions

1. Compiling the program

To build the release version, run these commands:

$ cd path/to/fractal
$ mkdir Release
$ cd Release
$ cmake -DCMAKE_BUILD_TYPE=Release ..
$ make

To build the debug version, run these commands:

$ cd path/to/fractal
$ mkdir Debug
$ cd Debug
$ cmake -DCMAKE_BUILD_TYPE=Debug ..
$ make

2. How to run the program

Run the executable too see the help message:

./fractal

Or run with some supported fractal:

./fractal mandelbrot

Note

For CUDA support, you need to install CMake version >= 3.24
If you want to disable CUDA support, just uncommnet line 19 in CMakeLists.txt file.

🌄 Screenshots

Mandelbrot

Julia

Burning Ship

Tricorn

Mandelbox

Multibrot

Mandelbar

Perpendicular Burning Ship

Celtic Mandelbrot