Henry Segerman is a mathematician who's been building brain-melting virtual world simulations for over a decade, and his latest project is quite possibly the most cerebral yet: A VR experience that simulates non-euclidean, negatively curved space, I.E., kinda like what space is like near a black hole:

This video demonstrates a virtual reality simulation of a non-euclidean, negatively curved space. Suppose that I walk in a straight line, then turn left by 90 degrees, and then repeat these steps until I get back to where I started. In a flat space with no curvature, I have just walked around a square. In a positively curved space, like the surface of a sphere, I could instead have walked around a right-angled triangle: I could start on the equator and walk a quarter the way around the sphere, then turn left and go up to the north pole, then turn left again and walk down to my starting point. In this video I am (virtually) in a negatively curved space; here I walk around a right-angled pentagon.

"The idea of space itself being curved has been around for a while," Segerman tells me, "most famously in Einstein's relativity. This is a way to experience a curved space in VR There are some phenomena that I knew would happen going into this kind of project, but experiencing it directly is a much more visceral understanding."

With some tweaks, he even thinks it could be used to teach Einstein's theories from a first-person perspective: "Our stuff so far doesn't do variable curvature as in relativity," he allows."The spaces we have are very nice uniform spaces; in relativity, the curvature changes as you move around. In principle, one could do something with variable curvature, but we're not doing that yet!"

You can check out a demo of this on WebGL site here, and the code to create the simulation is open source and available on GitHub here. The fact that other developers can play with this code opens up the possibility of using it to create other kinds of negatively curved space-based apps -- for instance, in a first-person shooter.