sergii-moroz / fractol

Fractol is a 42 School project. The purpose of this project is to create a fractal renderer.

fractol

Fractol is a 42 School project. The project designed to render and display various types of fractals in real-time. Fractals are complex mathematical structures that exhibit self-similarity at different scales. This project provides an interactive platform for users to explore and appreciate the beauty of these intricate mathematical patterns.

Quick Start

To quickly get started with Fractol, follow these steps:

1. Clone the Repository
2. Navigate to the Project Directory
3. Build the Project
4. Run Fractol

https://github.com/sergii-moroz/fractol.git
cd fractol
make
./fractol 1

Usage

for fractals type 1 - 3

./fractol 1

for Julia

./fractol 4 -0.6 0.6

Controls

ESC - quit the programm

arrows or A, W, S, D - move screen

SPACE - change color palette

1 to 0 - change complex constant $C$ (only for Julia fractal)

Numpad

+, - - increase or decrease the picture quality (number of iteration)

1 - Mandelbrot: $Z_{n+1} = Z_n^2 + C$

2 - Mandelbrot: $Z_{n+1} = Z_n^4 + C$

3 - Burning ship: $Z_{n+1} = |Z_n|^2 + C$. It really means $x + i y \to (|x| + i |y|)^2 + (a + i b)$. When expanded using usual algebra (including $i^2$ = -1), you get $x \to x^2 - y^2 + a$ and $y \to 2 |x| |y| + b$. link

4 - Julia: $Z_{n+1} = Z_n^2 + C$

Usefull links

Lodev Julia and Mandelbrot Tutorial ⭐

Fractals Generated by Complex Numbers