Fractals are mathematical structures under exploration and development in virtually every academic discipline and beyond: “besides mathematics and science, fractals have direct applications in many fields, including music, literature,...
moreFractals are mathematical structures under exploration and development in virtually every academic discipline and beyond: “besides mathematics and science, fractals have direct applications in many fields, including music, literature, visual art, architecture, sculpture, dance, technology, business, finance, economics, psychology, and sociology” (Frame & Mandelbrot, 2002, p. 4). Since fractal geometry today is “the only available language for the study of roughness, a concept that is basic and related to our senses, but has been the last to give rise to a science,” (Ibid., p. 11) and ‘roughness’ or unevenness or irregularity is a natural, universal tenet of thought and matter, the science behind fractal geometry unifying it across disciplines holds much promise.
The rise of a multidisciplinary discourse containing measurable -- and predictable – patterns of irregularity is attributed to fractal geometry with the seriousness and playfulness of mathematics at its root. Because of these fundamentals, the newness of the study of fractal geometry lends itself to extreme unpredictability. Since formulas and algorithms create fractal images and patterns, much of the fun and exploration of fractals lies in ability to experience new mathematical conjectures in anticipation of new discoveries.
Such an exploratory method has been developing across the disciplines with diverse jargon but one common language uniting them all, that being this staunchly predictable yet wildly unpredictable mathematical integrity of the fractal, dependent upon the available formula or algorithm used to suggest its creation and level of complexity.
We have yet to discover or unveil a serious application of fractal geometries related to patterns of irregularity in consideration of the work of Irwin Panofsky and the positing of iconography in art history, e.g., or in philosophy with study of Michel Foucault’s architecture of knowledge or history of insanity, which appear to naturally lend themselves to such interrogations.