Coding Challenge: Julia set

The coding challenge for this term's Computing Cafe is to provide the fastest possible implementation of the calculation of a Julia set in either C++ or Python (or both). We'll focus on a Julia set with a function of the form:

f(z) = z ^ n + r * exp(i * phi).

The animation will be created for N steps with angles phi uniformly distributed in [0,2 pi). For each step a csv file has to be written for each step of the animation (i.e. each fixed angle), containing the values in gridwidth points in both coordinates of the complex plane for -1.8 < x < 1.8 (same for y). The csv should store the number of iterations after which the cut-off condition |z| > 2.0 is fulfilled for each point. A cut-off after 300 iterations is to be applied.

The free parameters we'll choose at random, after the deadline are:

• n in the julia function
• r in the julia function
• N: number of steps for the animation
• gridwidth: number of steps for both x and y

An (very slow) example implementation can be found in example.py. The script plot_result.py will read in the csv files and create an animation from that. Code in example.py based on ["High Performance Python" by Miche Gorelick, Ian Ozsvald. O'Reilly 2014][http://shop.oreilly.com/product/0636920028963.do].