Fractal Geometry and Applications Research Group
Introduction of the Research Group
Fractals are the "irregular and fragmented" shapes that surround us, described by Mandelbrot as "irregular and/or fragmented in a repeating pattern at all levels". The attractors and invariant measures of deterministic and random iterated function systems (IFS) provide a precise mathematical model of this scale-invariant property. One of the main goals of our group is to understand the structure, regularity properties, and dimensions of the resulting geometric shapes and measures through various dimensional concepts and measures. Such fractal patterns occur naturally in many areas of the natural sciences, including mathematics. Another main goal of our group is to deepen these connections and apply fractal geometry.