Fractal geometry in the context of Hurst exponent

Benoit B. Mandelbrot (20 November 1924 – 14 October 2010) was a Polish-born French-American mathematician and polymath with broad interests in the practical sciences, especially regarding what he labeled as "the art of roughness" of physical phenomena and "the uncontrolled element in life". He referred to himself as a "fractalist" and is recognized for his contribution to the field of fractal geometry, which included coining the word "fractal", as well as developing a theory of "roughness and self-similarity" in nature.

In 1936, at the age of 11, Mandelbrot and his family emigrated from Warsaw, Poland, to France. After World War II ended, Mandelbrot studied mathematics, graduating from universities in Paris and in the United States and receiving a master's degree in aeronautics from the California Institute of Technology. He spent most of his career in both the United States and France, having dual French and American citizenship. In 1958, he began a 35-year career at IBM, where he became an IBM Fellow, and periodically took leaves of absence to teach at Harvard University. At Harvard, following the publication of his study of U.S. commodity markets in relation to cotton futures, he taught economics and applied sciences.

In fractal geometry, the Minkowski–Bouligand dimension, also known as Minkowski dimension or box-counting dimension, is a way of determining the fractal dimension of a bounded set ${\textstyle S}$ in a Euclidean space ${\textstyle \mathbb {R} ^{n}}$, or more generally in a metric space ${\textstyle (X,d)}$. It is named after the Polish mathematician Hermann Minkowski and the French mathematician Georges Bouligand.

To calculate this dimension for a fractal ${\textstyle S}$, imagine this fractal lying on an evenly spaced grid and count how many boxes are required to cover the set. The box-counting dimension is calculated by seeing how this number changes as we make the grid finer by applying a box-counting algorithm.

Hokky Situngkir (born February 7, 1978) is an Indonesian scientist who researches complexity theory at Surya University. He is the founder of the Bandung Fe Institute, a research institute for social complexity research. His academic activities include research regarding the aspects of fractal geometry in Indonesian Batik, mathematical aspects of Indonesian traditional folk songs and in the architecture of Borobudur, as well as Indonesian stock market analysis with econophysics alongside Indonesian senior physicist Yohanes Surya. Situngkir helped create the Indonesian Digital Library of Traditional Culture (Perpustakaan Digital Budaya Indonesia) in order to increase public access to information about the diversity of traditional Indonesian culture, for the further application of data sciences.