So it's been a while since I last posted anything to this blog, and I really want to change that. I recently created a series of mathematical animations, all based on the same function. But I wanted to do more than just share these animations, I wanted to explain how I made them and the interesting features I discovered in the process. I thought about making a video for this purpose, as there are plenty of educational channels on YouTube nowadays. But I’m not that great at public speaking, and I did not want my presentation to detract from the animations themselves. Thus I decided to write this blog post.
In this blog entry I attempt to explain how you can build a polynomial up from its roots. That is the points where the function equals zero. I then explain how this same technique can be used to build rational functions, and what this means in the complex plane. This is something I use to generate a lot of the abstract mathematical art that I share on Tumblr, Flickr, and Deviant Art. So if you are interested in duplicating my art style, or just reading the rest of my blog, this entry is essential.