In the sciences, one frequently comes across oddities which grab our attention visually, and are explained in the language of mathematics. Just so with the tautochrome curve ~ a geometric curve for which, in uniform gravity and zero friction, objects placed at any point along the curve will take the same amount of time to reach the bottom (see image above). It is a delicious paradox, and you don't have to understand calculus to enjoy watching the animation at the link above.
Consider a more complex system ~ the wind blowing across the surface of water, or fluids (air or water) of different densities/speeds at their interface. A Kelvin-Helmholt instability results, forming hypnotic, almost fractal-like swirling turbulence. You can see K-I instabilities in the cloud patterns where air masses of differing density or speed meet, e.g. the atmospheres of Earth or Saturn. You can also see them where dissimilar liquids meet. Click on the animation here for an example.
Lastly, and most grandly, check out 3D Galaxy Map, "a representation of our galaxy, the Milky Way. It contains an overview map of the Milky Way Galaxy as seen from above, and a map of the Orion Arm (where our Sun is located), showing its major structures. The Orion Arm map is divided into navigable 10 parsec sectors, where you can explore stars. It contains a total of 142,278 known stars, 478 planets, 1855 pulsars, 31 disks and 14 black holes. Planet, pulsar, and multiple stars' orbits can be observed by increasing and decreasing the speed. You can rotate/zoom/pan within each of the scenes for a better view. More information can be found by clicking on Features."