Related papers: "Fractal Expression" in Chinese Calligraphy
We stand at the foot of a significant inflection in the trajectory of scientific discovery. As society continues on its fast-paced digital transformation, so does humankind's collective scientific knowledge and discourse. We now read and…
Artists spent a great deal of time studying anatomy for precise rendering of the human body as well as light, shadows, and perspective for convincing representation of the three-dimensional world. But in many paintings, they also had to…
Discretization of curves is an ancient topic. Even discretization of curves with an eye toward differential geometry is over a century old. However there is no general theory or methodology in the literature, despite the ubiquitous use of…
A new type of sectional curvature is introduced. The notion is purely algebraic and can be located in linear algebra as well as in differential geometry.
In this paper, we state and prove a simple geometric interpretation of the degrees of freedom of a chi-square distribution. The general geometric idea goes back at least to Fisher in the 1920s, but the exact result does not appear to have…
I review the current status of Lattice QCD calculations and the progress that we have made in consolidating the 'lattice QCD revolution' of four years ago. Significant results from formalisms other than the improved staggered formalism,…
In mesoscopic systems conductance fluctuations are a sensitive probe of electron dynamics and chaotic phenomena. We show that the conductance of a purely classical chaotic system with either fully chaotic or mixed phase space generically…
Repeatedly folding a strip of paper in half and unfolding it in straight angles produces a fractal: the dragon curve. Shallit, van der Poorten and others showed that the sequence of right and left turns relates to a continued fraction that…
We collect 14 representative corpora for major periods in Chinese history in this study. These corpora include poetic works produced in several dynasties, novels of the Ming and Qing dynasties, and essays and news reports written in modern…
We investigate the classical evolution of a $\phi^4$ scalar field theory, using in the initial state random field configurations possessing a fractal measure expressed by a non-integer mass dimension. These configurations resemble the…
We prove the connectedness and calculate the diameter of the oriented graph of graftings associated to exotic complex projective structures on a compact surface S with a given holonomy representation of Fuchsian type. The oriented graph of…
Fractals offer the ability to generate fascinating geometric shapes with all sorts of unique characteristics (for instance, fractal geometry provides a basis for modelling infinite detail found in nature). While fractals are non-euclidean…
We discuss the repercussions of the development of infinitesimal calculus into modern analysis, beginning with viewpoints expressed in the nineteenth and twentieth centuries and relating them to the natural cognitive development of…
In the quantum statistical parton distributions approach proposed more than one decade ago, one imposes relations between quarks and antiquarks expressions, which lead to very specific properties for the antiquarks. These properties have…
A fractal approach to numerical analysis of electromagnetic space-time crystals, created by three standing plane harmonic waves with mutually orthogonal phase planes and the same frequency, is presented. Finite models of electromagnetic…
A graph drawn in a surface is a near-quadrangulation if the sum of the lengths of the faces different from 4-faces is bounded by a fixed constant. We leverage duality between colorings and flows to design an efficient algorithm for…
We show that when the standard techniques for calculating fractal dimensions in empirical data (such as the box counting) are applied on uniformly random structures, apparent fractal behavior is observed in a range between physically…
Analysis of the both type (flint-forward and crown-forward) achromatic doublets was carried out. The investigation revealed possible initial approximations which could be used by opticians at producing of the achromatic doublets in last…
Diffusive representations of fractional derivatives have proven to be useful tools in the construction of fast and memory efficient numerical methods for solving fractional differential equations. A common challenge in many of the known…
Until recently, Chinese texts could not be studied using co-word analysis because the words are not separated by spaces in Chinese (and Japanese). A word can be composed of one or more characters. The online availability of programs that…