These are called Liesegang rings. You’ve probably seen them on paper, in rocks and cliffs around you, and in test tubes. They were first discovered back in 1855, and we’re still working out the details. Learn (roughly) what makes these things happen.
Liesegang rings are, in the grand tradition of science, not named after the person who first discovered them. That was Friedlich Runge, a chemist whose work includes the discovery of caffeine and the practice of paper chromatography. It was chromatography that got him to discover these rings. He noticed that, when certain substances were combined on paper, they made concentric rings that spread outwards.
The rings bear the name of Raphael Liesegang, who discovered the reaction we see above. Put a drop of silver nitrate onto a drop of potassium dichromate in agar gel, and you get rings of silver dichromate. Do the same experiment in a test tube and you get layers of silver dichromate going down into the test tube.
The rings are a precipitate of the two chemicals, and they form according to the density of the mix. The density is not continuous. It builds and drops away, making rings (or layers) instead of an even mix.
Although we know that this happens, we still don’t know exactly why. Some people think it’s that the two chemicals create a supersaturation that has to become unstable before the rings form. Some think that the particles disperse throughout the gel but coagulate into rings.
These things don’t only happen in laboratories. If you’ve taken a walk and seen layers of dark stone marbling rocks and cliff sides, that’s not exclusively due to periodic changes in atmosphere or sedimentation building up over time. Some of those rocks are colored by Liesegang rings, and show how two chemicals put down at roughly the same time formed layers of precipitate.
[Source: A Short History of Liesegang Rings.]