I'm personally using Quil (http://quil.info/), a Clojure wrapper around Processing. It's a good tool. You can also use Processing (https://processing.org/) directly, if you prefer Java. There are other frameworks, but I'm less familiar with them. There's probably one for your preferred programming language!

Those patterns look very cool, and not that technically hard to technically do -- the artistry is the challenge with those.

Once you get the framework working, you can start thinking about what you want to do. Begin by doing simple things -- graph a plain circle of one color. Then add complexity and randomness.

Feel free to email me (email in profile) if you want more specific advice. (Offer open to anyone people reading this)