DeepDrill is a Mandelbrot generator based on perturbation and series approximation. With these new techniques, it is possible to explore the Mandelbrot set at zoom levels that are out of reach of traditional algorithms due to their rapidly increasing computation time. Many images that used to keep computers busy for weeks and months can now be calculated in a matter of minutes.


My first contact with the Mandelbrot set was in the mid-eighties, when the first affordable computers made their way into children’s rooms. Back then, fractal generators were popular programs to challenge the processing power and graphics capabilities of the machines we loved. I was quickly captivated by the colorful and intriguingly branching structures, although I was still too young to grasp the mathematical background to its full extend. Later, when school ended and my college years began, I moved on to other things and the world of fractals gradually disappeared from my daily life.

This changed all of a sudden when the YouTube algorithm suggested this Mandelbrot zoom video from Maths Town. At first, I couldn’t believe what I was seeing. On the one hand, I was amazed by the beauty in which the Mandelbrot set can be visualized nowadays. On the other hand, and this is the more important point, I was perplexed by how deeply this video zoomed into the Mandelbrot set. My first thought was that the computation of this video must have taken months if not years, but a quick research revealed that I was wrong. Hidden from my attention for years, clever mathematicians had succeeded in massively speeding up the calculation of the Mandelbrot set with novel algorithms. Combined with the computing power of modern computers, it is now possible to represent the set in a beauty and level of detail that hardly anyone had considered possible back in the day.

After delving deeper into the new algorithms, I came up with the idea of combining my new insights with my lecturing work. The result is DeepDrill. This much in advance: I do not want to compete with the established fractal generators in any way. The established generators are so far developed that I am neither able to compete in functionality nor in computing speed. With DeepDrill, I am trying to provide a lean and easy-to-comprehend code base that allows students to learn modern Mandelbrot algorithms from a concrete implementation. It is meant to serve as a base application that can be expanded by various student projects in the areas of numerics, computer graphics, and runtime optimization. If my idea falls on fertile ground, the functionality will gradually expand.


DeepDrill is open-source and published under the terms of the GNU General Public License v3.