Jeffrey weeks has a great website with games visualizing 3-manifolds. The film Not Knot is great for the same purpose.
Has anyone created software or a movie demonstrating the effects of Lorentz contraction? I imagine something modeling where you fly through a world with clocks and meter sticks and can alter your speed to be close to the speed of light.
Does anyone now if this exists?
Yes! There is a great game created by the MIT games lab called A Slower Speed Of Light that does an excellent treatment of relativistic effects, including the Doppler effect and Lorentz Contraction.
The game is fully interactive and the player gets to see the effects of relativity gradually unfold. The player collects a series of orbs, and each orb lowers the speed of light in the game. As the game's speed of light approaches the player's maximum walking speed, the relativistic effects become more obvious.
You can see a video and download the game here: http://gamelab.mit.edu/games/a-slower-speed-of-light/