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In 1854, Michael Faraday wrote to thank the author who had sent him a book on the art of paper marbling. In the letter, Faraday referred to `the very beautiful principles of natural philosophy' involved in the process of dropping ink on thickened water. What are the `beautiful principles' that Faraday referred to, and how are they involved in the art of paper marbling? Here I consider some of the physical processes that occur in paper marbling and how the patterns that emerge represent `dissipative structures' that are governed by fundamental principles of nature, in particular the tendency for physical systems to minimize their free energy. Similar principles informed the theories of perception and aesthetic appreciation developed by the founders of the Gestalt school of psychology in the early twentieth century, which were inspired by Faraday's work on magnetic fields. I suggest that combining these theories with the insights from thermodynamics offers a fertile approach for understanding the relationship between fundamental principles of nature and art.