title: Edges of Saturn's rings are fractal.
abstract: The images recently sent by the Cassini spacecraft mission (on the NASA website http://saturn.jpl.nasa.gov/photos/halloffame/) show the complex and beautiful rings of Saturn. Over the past few decades, various conjectures were advanced that Saturn's rings are Cantor-like sets, although no convincing fractal analysis of actual images has ever appeared. Here we focus on four images sent by the Cassini spacecraft mission (slide #42 "Mapping Clumps in Saturn's Rings", slide #54 "Scattered Sunshine", slide #66 taken two weeks before the planet's Augus't 200'9 equinox, and slide #68 showing edge waves raised by Daphnis on the Keeler Gap) and one image from the Voyager 2' mission in 1981. Using three box-counting methods, we determine the fractal dimension of edges of rings seen here to be consistently about 1.63 ~ 1.78. This clarifies in what sense Saturn's rings are fractal.
authors.affiliation: Division of Engineering and Applied Science, California Institute of Technology, 91125 Pasadena, CA USA.
authors.forename: Jun
authors.initials: J
authors.lastname: Li
authors.affiliation: Department of Mechanical Science & Engineering, Institute for Condensed Matter Theory and Beckman Institute, University of Illinois at Urbana-Champaign, 61801 Urbana, IL USA.
authors.forename: Martin
authors.initials: M
authors.lastname: Ostoja-Starzewski
keywords: Cassini mission; Fractals; Ring divisions; Saturn’s rings