If you've ever seen or played Geometry Wars, imagine a relaxed version in 3D, and you'll have a reasonable idea of Polynomial.
The Polynomial demo features eleven 3D arenas, all made from mathematically-generated fractal scenery. These glowing arenas are really pretty to look at, and you can spend quite a while just flying around in Polynomial's easy mode, admiring the sights. If you want more disorientating visuals, press the Esc key and enable the Dynamic Reactor for a weird color changing effect that the developer warns may induce dizziness!
The aim of Polynomial is high scores, achieved through shooting the red enemies on your radar. With difficulty on Insane level, it really is fast-paced and intense, but on the easier levels it's not too difficult. The controls, using the WASD keys and the mouse are fine, and aren't complicated enough to distract you from the graphics.
Polynomial is quite an abstract shooter experience, but it's so attractive you probably won't care!