#complex-number

Today’s fractal is the famous Mandelbrot Set. The Mandelbrot set is a well-known and complex mathematical set often associated with fractals and chaos theory. Named after the mathematician Benoît B. Mandelbrot, it’s a set of complex numbers defined by a simple iterative process. The Mandelbrot set is an intricate and self-similar boundary, which reveals increasingly complex patterns at different magnifications. On the other hand, I heard the term “The fingerprint of God” in some sources resembling its aesthetic and philosophical…

Today’s fractal is the Julia Set, the amazing simplicity of chaos. There are lots of applets and articles on the internet about this fractal. You can generate this with the iteration of a basic function many times and placing points on the complex plane. I developed a Grasshopper implementation in 2012. Also, this was my first study on complex numbers. At each iteration, the detail level increases. I utilized a common brute-force approach, distributing a grid of points, converting them…

Studying circle packing led me back to my high school 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 packing. After finding an old post by Daniel Piker,  I’m truly enlightened about an old topic of our high school education: The complex numbers! Then I found this link, explaining the…