fract-ol

This project is about creating fractals graphically.

The term fractal was first used by mathematician Benoit Mandelbrot in 1974. He based it on the Latin word fractus which means "broken" or "fractured".

A fractal is an abstract mathematical object, like a curve or a surface, which pattern remains the same at every scale.

This projects uses the 42 school graphical library: the MiniLibX. This library was developed internally and includes basic necessary tools to open a window, create images and deal with keyboard and mouse events.

Mandelbrot Set

The Mandelbrot Set is defined by iterating the following function:

$z_{n+1} = z_{n}^2 + c$

where $z$ and $c$ are complex numbers. The Mandelbrot Set consists of all complex numbers $c$ for which the iteration does not diverge to infinity when starting with $z = 0$.

Julia Set

The formula defining the Julia Set is similar to that of the Mandelbrot Set:

$z_{n+1} = z_{n}^2 + c$

However, in the Julia Set, $c$ remains constant, and the set is determined by the behavior of the iterates $z$.

Burning ship fractal

The Burning Ship Fractal is a variant of the Mandelbrot Set, known for its distinctive "ship-like" structures that emerge from the iterative process. The formula defining the Burning Ship Fractal is:

$z_{n+1} = (|Re(z_n)| + i|Im(z_n)|)^2 + c$

Similar to the Mandelbrot Set, the Burning Ship Fractal is generated by iterating complex numbers and determining whether the sequence remains bounded or tends towards infinity.

Multibrot set

The Multibrot Set generalizes the Mandelbrot Set by considering higher powers in the iteration formula. While the Mandelbrot Set corresponds to the case where the exponent is 2, the Multibrot Set explores the behavior of the iteration for exponents greater than 2. The formula defining the Multibrot Set is:

$z_{n+1} = z_{n}^p + c$

where $p$ represents the exponent.

Julia Burning Ship set

The Julia Burning Ship Fractal is a variant of the Julia Set. The formula defining the Julia Burning Ship Fractal is: $z_{n+1} = (|Re(z_n)| + i|Im(z_n)|)^2 + c$

Similar to the Julia Set, the Julia Burning Ship Fractal is generated by iterating complex numbers and determining whether the sequence remains bounded or tends towards infinity.