I've been using Python to analyze the majority of my research data, so was very excited when the IPython Notebook was released at the end of last year. Over the last few months, I've been learning how to use the Notebook and transitioning some of my new research data to this interactive format. And what better way to learn a new programming system than by making fractals?
Here's a screenshot of the notebook interface used to plot the Bifurcation Diagram. I know it's not really a fractal, but we'll get there. Note that most of the code is standard Python, yet IPython commands like %time can be used too. Results are then showed right in the browser window, inline with the code! The notebook can be downloaded here.
Next is the famous fern fractal, and its notebook code.
But then, as usual, I went a little overboard, and started trying fractals involving orbit traps, multiple colors, and unusual coloring schemes. Here's a sample of the fractal art I've thrown together.