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Mandelbrot Generator:
Using Java

about the project...

I learned about the Mandelbrot set in the Fall of 2019 in my CMSC131 course on object-oriented programming. A Mandelbrot set is an aesthetic mathematical visualization created by applying mathematical rules to a set of complex numbers. These iterations produce fractals that are exciting to look at. I have always been intrigued by the concept of using mathematics to create art, so I decided to create my own Mandelbrot set generator. This generator produces uniquely beautiful Mandelbrot set visualizations in each run.

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the process:

1. research

To begin this project, I researched the Mandelbrot set in detail. I learned that the Mandelbrot set was discovered by a mathematician named Benoit Mandelbrot in 1979. Additionally, the Mandelbrot set consists of fractals. Fractals have a unique property that allows us to zoom in an infinite number of times. Below is an example of a fractal...

https://www.artforum.com/print/202109/caroline-a-jones-on-the-art-of-tauba-auerbach-86938

We can discover more details about the shape with each zoom. In the Mandelbrot set that I created, a fractal is an image that represents the boundary between the Mandelbrot set and the colored portion.

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Next, I researched the mathematical computations used to create the Mandelbrot set. I learned that the Mandelbrot set is produced by using complex numbers as starting values. The following computations are applied to those starting values to produce a sequence...

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Some of these starting values produce a diverging sequence. The Mandelbrot set is the set of all the starting values that don't produce diverging sequences. Once we have computed the Mandelbrot set, we can graph our results. We can use a Cartesian plane where each point in the plane represents a complex number. All the points in the Mandelbrot set will be set to black, while the other points are set to a random color. The resulting graph is a unique Mandelbrot visualization. 

2. coding and testing

Once I established the process of creating a Mandelbrot set, I started writing methods for each step. I wrote methods to calculate the Mandelbrot set and display the set on a GUI. I also added a feature that allows the user to select a color scheme for their personalized Mandelbrot set. The user can define their own set of colors, use red and white bands or select a pre-defined crazy color scheme. The user also has the option to select the maximum number of iterations to check for divergence. 

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I tested my code after writing each method to ensure the methods worked correctly. Once I finished programming the application, I conducted final tests to check that the GUI worked as intended. The end result was a working Mandelbrot set generator that allows users to create special visualizations.

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© 2023 By Ashwittha Ganesan.

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