Fractol is a project that explores the fascinating world of fractals and complex numbers. It allows you to generate and explore various types of fractals in real-time, providing an interactive and visually stunning experience.
Fractol is a project developed as part of the 42 curriculum to deepen your understanding of fractals and complex numbers. It provides a graphical interface where you can interactively explore and generate different types of fractals.
Fractals have applications in various fields, including mathematics, physics, computer graphics, and art. They are used to model natural phenomena, simulate complex systems, and create visually stunning images and animations.
In the Fractol project, you will have the opportunity to explore and generate different types of fractals, such as the Mandelbrot set and Julia set fractal. The project provides a graphical interface where you can interactively navigate through the fractal space, zoom in and out, and adjust parameters to modify the appearance of the fractals.
To run the Fractol project, make sure you have the necessary dependencies installed, such as the graphics library (e.g., OpenGL) and any additional libraries required by the project. Once the project is running, you can use the keyboard and mouse controls provided by the interface to interact with the fractals and navigate through the visualizations.
Feel free to explore different fractal types, adjust parameters, and observe the intricate patterns that emerge. The fractal dimension is another interesting aspect to consider, as it relates to the complexity and self-similarity of the fractals.
Contributions to the Fractol project are welcome! If you have any improvements, bug fixes, or additional features to add, feel free to submit a pull request. Please follow the existing code style and provide clear documentation for your contributions.
- Fractals Generated by Complex Numbers
- Mathematics and the Arts: Fractals
- Generating Fractals with Complex Numbers
Complex numbers, on the other hand, consist of a real part and an imaginary part. They are represented in the form a + bi, where a is the real part, b is the imaginary part, and i is the imaginary unit. Complex numbers play a crucial role in generating fractals. The interaction between complex numbers and iterative functions is what creates the intricate patterns and structures in fractals.
The Mandelbrot set is a well-known fractal generated using complex numbers with a recursive sequence. It is created by iterating a simple recursive rule using complex numbers. The boundary of the Mandelbrot set exhibits quasi-self-similarity, where portions of it look very similar to the whole. The iteration formula used in the Mandelbrot set is:
Z = Z^2 + C Here, Z and C are complex numbers. The start value for Z is always 0, and C is the constant part that determines the location of the iteration series in the complex plane.
By manipulating the complex numbers and applying mathematical operations, you can explore different regions of fractals and discover hidden details. The arithmetic operations on complex numbers, such as scaling or rotation, can be graphically represented to understand their impact on the generation of fractals.
The Fractol project utilizes the MLX library, which is a simple graphics library developed at 42. MLX provides functions for creating windows, handling events, and drawing basic shapes on the screen. It is used to create the graphical interface for the Fractol project.
To run the Fractol project, make sure you have the necessary dependencies installed, such as the graphics library (e.g., OpenGL) and any additional libraries required by the project. Once the project is running, you can use the keyboard and mouse controls provided by the interface to interact with the fractals and navigate through the visualizations.
To run the Fractol project, follow these steps:
- Clone the repository to your local machine.
- Navigate to the project directory.
- Run the
makecommand to compile the project. - Execute the generated executable file.
Make sure you have the necessary dependencies installed, such as the graphics library (e.g., OpenGL) and any additional libraries required by the project.
Once you have the Fractol project running, you can use the graphical interface to explore and generate fractals. The interface allows you to navigate through the fractal space, zoom in and out, and adjust parameters to modify the appearance of the fractals.
Experiment with different fractal types, explore different regions of the fractal space, and observe the intricate patterns that emerge. Use the keyboard and mouse controls provided by the interface to interact with the fractals and navigate through the visualizations.