Saturn is perhaps most famous for the ring that it has around itself. Originally, it was believed that the ring is a single one. After some time, a break in the middle was discovered, and scientists considered it to have 2 rings. However, when Voyager I approached Saturn, it discovered that the two ring were also broken in the middle, and the 4 smaller rings were broken as well. Eventually, it identified a very large number of breaks, which continuously broke even small rings into smaller pieces. The overall structure is amazingly similar to... Cantor Set, which is formed by continuously cutting out middles of the segments:

If you put circles through the points in the last picture above, you will get a simple model of the rings of Saturn: