complex number

This is the set of all Julia Sets (studied here). Here is a simple explanation without math. According to this website: The Mandelbrot set, named after Benoit Mandelbrot, is a fractal. Fractals are objects that display self-similarity at various scales. Magnifying a fractal reveals small-scale details similar to the large-scale characteristics. Although the Mandelbrot set is self-similar at magnified scales, the small scale details are not identical to the whole. In fact, the Mandelbrot set is infinitely complex. Yet the process of generating it is based on an extremely simple equation involving complex numbers. […]

I’m completely stuck with fractals nowadays, especially famous Mandelbrot and Julia sets. Here is my first definition which estimates Julia sets. There are lots of applets about this fractal calculations on the internet because the computational method is very simple, (and generally people love them because of this dilemma between simplicity, chaos and infinity). It is the iteration of a single function over and over again and placing points on the complex plane (not the cartesian plane). Here, it was my first recall of complex numbers, now I’m happy I’ll […]

Studying circle packing led me back at the highschool days. First, I’ve tried to write a vb.net component so that I would say Grasshopper to place circles and check lots of things iterating again and again. Then I felt that this was not my real interest in circle packings. After finding an old post of Daniel Piker (here),  I’m truly enlightened about an old topic of our highschool education: The complex numbers! Then I found this link, explaining the short history and meaning of complex numbers for geometry. My first […]