# Fractal Geometry **Domain:** Mathematics / Complexity / Natural Form **Doc Type:** Concept Node **Maturity:** Evolving **Related:** [[Benoît Mandelbrot]], [[Scalar Nesting]], [[Complex Systems]], [[IBM Research]] ## Definition **Fractal geometry** studies forms whose irregular structure can recur or remain statistically related across changes of scale. It provides mathematical tools for objects that classical smooth geometry describes poorly, including coastlines, turbulence, branching structures, and clustered noise. ## Yorktown Context [[Benoît Mandelbrot|Mandelbrot’s]] investigation of transmission noise at the [[IBM Thomas J. Watson Research Center]] helped him recognize scale-recurring structure inside apparently chaotic signals. Computer graphics and IBM’s research environment later helped make these forms visible and mathematically tractable. ## Ontological Function Fractals connect [[Scalar Nesting]] to [[Complex Systems]]. Repetition across scale does not imply exact identity, and visual similarity is not by itself proof of one generating mechanism. The concept is useful precisely when paired with evidence about the process producing the pattern. ## Sources / Provenance - IBM, “Fractal geometry”: https://www.ibm.com/history/fractal-geometry