What you're seeing above is a video of a study done by Sandra Zetina and Roberto Zenit, at the National Autonomous University of Mexico. They were studying a technique pioneered by painter David Alfaro Siquieros, who used the mixing of different densities of paint in his paintings. It was a technique he called "accidental painting." Outside of the art world it is called Rayleigh-Taylor instability.
The instability comes from the different densities of the paint. The white paint is denser, and so when it's poured on top of the black paint, blobs of it tunnel down into the black paint. These become pockets and expand, while some dense white paint is still on the surface. The paints do mix, but not completely or regularly. This is Rayleigh-Taylor instability.
The paintings are hardly the only example. Rayleigh-Taylor instability creates these pockets of one density separated by long, spindly fingers of another density all over the natural world. It's seen in the ocean and in the atmosphere, where, for reasons of temperature or salinity, denser gas and liquid is occasionally dumped over less-dense material and tunnels downwards, just like the paint. In space, stars extrude denser material over lighter material all the time, and sometimes denser material can be on the outside of a nebula, being drawn inwards by a source of gravity. All of these will display the same instability as paint mixing. Tf you want to do this at home, and don't want paint everywhere, colored oil and water, or milk and molasses work just as well.
Crab Nebula Image: NASA, ESA, J. Hester (Arizona State University)