Mandelbrot Set Generator

Description

This repository contains a Julia program that generates static images of the Mandelbrot Set, a fascinating fractal. The program allows you to explore and visualize the beauty of the Mandelbrot Set by generating static images in different colorways.

NOTE: It is planned to include a zoom-function to explore the fractal in depth in further versions of this program. By now, it only generates static images.

How the Mandelbrot Set is Calculated and Colored

The Mandelbrot Set is defined using an iterative process. For each point in the complex plane, the program repeatedly applies a mathematical formula:

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

Where:

• z_n is an initial complex number (usually starting at 0).
• c is the complex number corresponding to the point being tested.

The program iterates this formula until one of two conditions is met:

1. The absolute value of z_n becomes larger than a predefined threshold (e.g., 3), indicating that the point is likely not in the Mandelbrot Set, and the iteration is terminated. => Points are colored based on how many iterations we need to exceed the threshold (colormap).
2. The maximum number of iterations is reached without z_n exceeding the threshold, in which case the point is assumed to be in the Mandelbrot Set. => Points turn black.

For further information, refer to: Mandelbrot Universität Leipzig

How the Code Works

The code in this repository utilizes the Julia language to perform the following steps:

• Define a range of complex numbers in the complex plane to create an image.
• For each complex number, apply the Mandelbrot Set calculation with a maximum number of iterations.
• Based on the number of iterations required for divergence, assign colors to the corresponding points.
• Save the resulting image as a bitmap (BMP) file.

The color assignment is done using a color map, where the number of iterations determines the color of each point. The exact colors and color scheme can be customized based on preferences.

Installation

To run this project, you'll need to have Julia installed on your computer. If you don't have Julia installed, you can download it from the official Julia website.

Follow these steps to install and run the project:

1. Clone this repository to your local machine:

   bash
   git clone https://github.com/your-username/mandelbrot-set-generator.git
   

2. Navigate to the project directory:

cd mandelbrot-set-generator

3. Install the required Julia packages by running the following commands within the Julia REPL (enter "]" to activate package manager mode):

using Pkg
Pkg.activate(".")
Pkg.instantiate()

4. Run the Mandelbrot Set generator:

include("MandelbrotZoom.jl")  # Replace with the actual name of your Julia script

5. The generated Mandelbrot Set image will be saved as mandelbrot_set_nozoom.bmp.

Acknowledgements

Got my code inspiration from opensources (YT) explanation of the Mandelbrot code in Julia: opersources YouTube Channel

Got the idea for Zooming and how I might do it from Alex Carney (YT) who explains it for P5.js: Alex Carney YouTube Channel

TY :-)