Decalcomania

Fractal paint patterns are easily made by a process related to viscous fingering.

As the sheets separate, paint adheres to both the top and bottom, forming ridges between the papers.

With increasing distance between the papers, the paint ridges coalesce and a branching pattern appears.

As more and more ridges coalesce, a dendritic fractal forms. Here is an example.

Click the picture to reduce.

Here are some examples, including recent student projects.
Here are some historical precedents from art.