This is a new and interesting way to add more detail to simulated fluids like smoke. Even if it’s far from realtime, some idea´s might be useful in games too.
The link to the paper:
http://www.cs.cornell.edu/~tedkim/WTURB/wavelet_turbulence.pdf
The best algorithm to generate a point in a circle is to generate a point in a square with the same width as the circle diameter and then rerun the algorithm until this random point is inside the circle. This algorithm might need to run a couple of times before finding a suitable point but will be faster than a more algorithmic solutions.
Pseudo code:
