Complex Numbers

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 (here),  I’m truly enlightened about an old topic of our high school education: The complex numbers! Then I found this link, explaining the short history and meaning of complex numbers for geometry.

My first try was the T(z) = z+k/z transformation of a simple square grid. This transformation is said to be studied for the aerodynamics of airfoils.

In this animation, I’m playing with the real number k and the initial square grid, and applying an equation to the complex number generated from x and y coordinates, then re-construct the square grid back again. Such transformations are called holomorphic transformations. From now on, complex number components are my friends. Things are becoming much easier with them. Here is my first working file: [GHX: 0.9.0006]