Related papers: Was Benoit Mandelbrot a hedgehog or a fox?
This text revisits the origins of econophysics through the figure of Beno\^it Mandelbrot, not as the father of fractals, but as the instigator of a distinctive scientific posture. The guiding thread is methodological: accept the stubborn…
B. Mandelbrot gave a new birth to the notions of scale invariance, selfsimilarity and non-integer dimensions, gathering them as the founding corner-stones used to build up fractal geometry. The first purpose of the present contribution is…
For words, rank-frequency distributions have long been heralded for adherence to a potentially-universal phenomenon known as Zipf's law. The hypothetical form of this empirical phenomenon was refined by Ben\^{i}ot Mandelbrot to that which…
We suggest an approach to constructing physical systems with dynamical characteristics of the complex analytic iterative maps. The idea follows from a simple notion that the complex quadratic map by a variable change may be transformed into…
Duerer's engraving ``MELENCOLIA I'' was circulated in two versions not previously distinguished. Besides their conspicuous early Renaissance scientific instruments and tools, they contain numerous apparently unreported concealments whose…
Scholars are often categorized into two types: hedgehogs (specialists), who focus on working within a specific research field, and foxes (generalists), who actively contribute to a variety of fields. Despite the familiar anecdotes and…
Mandelbrot set arose from the pioneering work of French mathematician Gaston Julia in the field of complex dynamics at the beginning of the 20th century. French-American mathematician Benoit Mandelbrot used computers to calculate iterations…
The Mandelbrot set is an extremely well-known mathematical object that can be described in a quite simple way but has very interesting and non-trivial properties. This paper surveys some results that are known concerning the…
A curious observation was made that the rank statistics of scientific citation numbers follows Zipf-Mandelbrot's law. The same pow-like behavior is exhibited by some simple random citation models. The observed regularity indicates not so…
Although fractional Brownian motion was not invented by Benoit Mandelbrot, it was he who recognized the importance of this random process and gave it the name by which it is known today. This is a personal account of the history behind…
Long memory plays an important role in many fields by determining the behaviour and predictability of systems; for instance, climate, hydrology, finance, networks and DNA sequencing. In particular, it is important to test if a process is…
Towards the end of the last century, B. Mandelbrot saw the importance, revealed the beauty, and robustly promoted (multi-)fractals. Multiplicative cascades are closely related and provide simple models for the study of turbulence and chaos.…
Extensive confusion exists and persists in the literature on dynamical systems theory, cosmology, and other fields over spectra of fractal dimensions. Entirely different generating functions have been treated as if they should yield…
Our first experience of dimension typically comes in the intuitive Euclidean sense: a line is one dimensional, a plane is two-dimensional, and a volume is three-dimensional. However, following the work of Mandelbrot \cite{mandelbrot},…
In this paper the Zipf-Mandelbrot law is revisited in the context of linguistics. Despite its widespread popularity the Zipf--Mandelbrot law can only describe the statistical behaviour of a rather restricted fraction of the total number of…
The sciences of complexity present some recurrent themes: the emergence of qualitatively new behaviors in dissipative systems out of equilibrium, the aparent tendency of complex system to lie at the border of phase transitions and…
This paper critically examines the central thesis of Kieran Fox's "I Am a Part of Infinity: The Spiritual Journey of Albert Einstein"-namely, that Einstein's intellectual development constitutes a coherent spiritual path culminating in a…
Self-similarity is a property of fractal structures, a concept introduced by Mandelbrot and one of the fundamental mathematical results of the 20th century. The importance of fractal geometry stems from the fact that these structures were…
Niels Bohr's doctrine of the primacy of "classical concepts" is arguably his most criticized and misunderstood view. We present a new, careful historical analysis that makes clear that Bohr's doctrine was primarily an epistemological…
The article presents a new interpretation for Zipf-Mandelbrot's law in natural language which rests on two areas of information theory. Firstly, we construct a new class of grammar-based codes and, secondly, we investigate properties of…