Although a couple years old (2010), this result is still quite a breakthrough: Socolar and Taylor have constructed a single, painted tile that when assembled correctly, can only produce an aperiodic tiling of the plane. These are some images from the paper:
Mesh will be calling the Fields Institute home for the immediate future! With hundreds of world class mathematicians visiting, researching, lecturing, or just chatting at this great (and great looking) institution, I could hardly ask for a more appropriate office location.
Although by no means the bleeding edge of SPH simulations, it does implement a tweaked Kd-Tree search for n nearest neighbours, the standard SPH functions (kernels, viscosity, and pressure), and runs at interactive rates.
Click on the image to try it out: