2026-07-072026-07-07http://salesiana.dossiersoluciones.com/handle/123456789/151570A theory is developed of the intricately fingered patterns of flux domains observed in the intermediate state of thin type-I superconductors. The patterns are shown to arise from the competition between the long-range Biot-Savart interactions of the Meissner currents encircling each region and the superconducting-normal surface energy. The energy of a set of such domains is expressed as a nonlocal functional of the positions of their boundaries, and a simple gradient flow in configuration space yields branched flux domains qualitatively like those seen in experiment. Connections with pattern formation in amphiphilic monolayers and magnetic fluids are emphasized.11 pages, 2 figs (available from authors), REVTex 3.0Condensed MatterPattern Formation and Solitonstext