The game Gravity Pods is a very fun game, and it vividly illustrates the principle of sensitive dependence on initial conditions. You're asked to fire a projectile in an area which includes some gravitational attractors, in an attempt to hit a given target. (At later levels you can move some of the attractors around. At even later levels there are repulsive objects, a nice twist. There might be even more tricks later, but I haven't gotten that far.)
It was an even more vivid illustration of sensitivity before, because in earlier incarnations of the game there were levels that could not be beaten -- it would be possible to fire at an angle of 10 degrees from the horizontal, or 10.1 degrees (0.1 degrees is the finest control you get over the angle at which the projectile is fired), but 10.05 degrees (say) is what you really needed. Similarly, the movable attractors and repellers can only be placed to the nearest pixel. I don't think this problem exists any more, but there are still annoying (although perhaps fascinating as well) levels in which sub-pixel positioning abilities would be nice.