The fractals is a rough and fragmented geometric shape that can be split into parts, and each of which is a similar reduced-size copy of the whole. It is a geometric object that has self-similar structure and exhibits more and more details the more we zoom in.
The fractals was discovered by Benoît Mandelbrot in 1950s and the term "Fractals" was coined by him in 1975. For more than two thousand years since ancient Greek, people studied smooth behavior using equations that assume that everything evolves in a very regular fashion.
Somehow, Mandelbrot was attracted to the irregularities of the nature and studied phenomena that belong to very different organized sciences but have the common characteristic of being irregular and fragmented at many scales. Fractal examples in the nature include lightning, clouds, crystals, snow flakes, mountain ranges, river networks, coastlines, cauliflower, broccoli, etc.……
The most famous and well-studied fractal is the Mandelbrot set. Many Mandelbrot set zoom videos are available online, and here are some interesting examples: video 1, video 2, video 3, and video 4.
Students are encouraged to generated a series of Mandelbrot set zoom images (or even videos) based on the given C++ code. Here are some extra project-related resources which may help you implement the project:
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