Foreground and Background: Fractal Unity of Art and Science

Joseph O'Neill^1,2*Iliyan Ivanov^3,4Giselle M Petzinger⁵Michael W Jakowec⁶

• ¹Division of Child Psychiatry, UCLA Semel Institute, Los Angeles, CA, United States
• ²UCLA Brain Research Institute, Los Angeles, CA, United States
• ³Icahn School of Medicine at Mount Sinai Department of Psychiatry, New York, United States
• ⁴CARES and FuTuReS Program, Mount Sinai St. Luke’s Hospital, New York, NY, United States
• ⁵Department of Neurology, USC Keck School of Medicine, Los Angeles, CA, United States
• ⁶University of Southern California Alfred E Mann School of Pharmacy and Pharmaceutical Sciences, Los Angeles, United States

In the last 50 years, fractals have been embraced by both artists and scientists. Here we link fractals to the question: What is the relationship between art and science? Clearly, both results of scientific experiments and expressions made by artworks contain mixed truth and falsity. Reflection shows that, in artistic expression, the public experiences falsity (the artifice) in the foreground and discovers truth in the background; while in science the opposite is applies. This is captured by the dictum: "Art is the lie that tells the truth/science the truth that lies." Truth behind lies or lies behind truth are revealed as one examines deeper and deeper levels. We modelled this progressive intermingling of truth and falsity in art and science with a fractal metaphor. In the metaphor, falsity (the artist's or scientist's subjective input) is the fractal frame (its interdigitated void spaces) while truth (Nature's objective response) is the fractal fill (its positive spaces). Using a simple fractal (the Cantor Dust) we worked-out an elementary formalization of this concept of "fractal truth" on an example problem (shallow-bed filtration). To assess possible presence of fractal character within art and science, we cast two hypotheses: H1: Both art and science exhibit one or more fractal properties; H2: Art and science manifest these properties in contrasting foreground/background manner. We tested H1-H2 using a formal comparative analysis. Thereby, we identified five general properties of fractals: dimensions, infinity/the infinitesimal, novelty/familiarity, ellipsis (gaps in representation), and the personal (role of the individual fractal analyst, artist, or scientist) illustrating each with example fractals (e.g., Koch Snowflake, Sierpiński Triangle, Pascal Triangle Modulo 5, Mandelbrot Set, Weierstraß Function). Comparing art and science, we found all five properties were present in both disciplines and that all five manifested in a contrasting foreground/background manner in art vs. science. We compare this fractal picture with prior notions of truth in art and science and suggest possible applications. We conclude a fractal perspective might promote a more unified and harmonious understanding of art and science on this Golden Fractal Anniversary.