Related papers: "Fractal Expression" in Chinese Calligraphy
We consider the theory of fluctuations of a colloidal solid observed in a confocal slice. For a cubic crystal we study the evolution of the projected elastic properties as a function of the anisotropy of the crystal using numerical methods…
In this note we outline the history of q-deformations; indicate their physical shortcomings; suggest their apparent resolution via an invariant formulation based on a new mathematics of genotopic type; and point out their expected physical…
In point of fact the Indian tradition in mathematics is long and glorious. It dates back to earliest times, and indeed many of the Indian discoveries from 5000 years ago correspond rather naturally to modern mathematical results.
The authors consider the Orthodox iconography of Byzantine style aimed at examining the existence of complex behavior and fractal patterns. It has been demonstrated that fractality in icons is manifested as two types: descending and…
This paper presents a preliminary version of the deformation theory of expressions of elements of algebras. The notion of *-functions is given. Several important problems appear in simplified forms, and these give an intuitive bird's-eye of…
Fractional calculus is a generalization of classical theories of integration and differentiation to arbitrary order (i.e., real or complex numbers). In the last two decades, this new mathematical modeling approach has been widely used to…
In this paper we study smooth solutions to a fractional mean curvature flow equation. We establish a comparison principle and consequences such as uniqueness and finite extinction time for compact solutions. We also establish evolutions…
We have performed detailed multifractal analysis on the minutely volatility of two indexes and 1139 stocks in the Chinese stock markets based on the partition function approach. The partition function $\chi_q(s)$ scales as a power law with…
Fractal behaviour, i.e. scale invariance in spatio-temporal dynamics, have been found to describe and model many systems in nature, in particular fluid mechanics and geophysical related geometrical objects, like the convective boundary…
As an important symbol of civilization and culture, architectures originally were built for sheltering human beings from weather disasters and therefore should be affected by climate change, particularly the associated change in the…
In this paper, we present a novel system (denoted as Polaca) to generate poetic Chinese landscape painting with calligraphy. Unlike previous single image-to-image painting generation, Polaca takes the classic poetry as input and outputs the…
It is known that there exists a function interpolating a given data set such that the graph of the function is the attractor of an iterated function system which is called fractal interpolation function. We generalize the notion of fractal…
The form factor of a quantum graph is a function measuring correlations within the spectrum of the graph. It can be expressed as a double sum over the periodic orbits on the graph. We propose a scheme which allows one to evaluate the…
The Tang (618 to 907) and Song (960 to 1279) dynasties witnessed an extraordinary flourishing of Chinese cultural expression, where floral motifs served as a dynamic medium for both poetic sentiment and artistic design. While previous…
The principle goal of computational mechanics is to define pattern and structure so that the organization of complex systems can be detected and quantified. Computational mechanics developed from efforts in the 1970s and early 1980s to…
Automatic character generation is an appealing solution for new typeface design, especially for Chinese typefaces including over 3700 most commonly-used characters. This task has two main pain points: (i) handwritten characters are usually…
Patterns formed by the flow of an inhomogeneous fluid (suspension) over a smooth inclined surface were studied. It was observed that for inclination angle larger than a threshold, global fractal patterns are formed. The fractal dimensions…
A painting consists of objects which are arranged in specific ways. The art of painting is drawing the objects, which can be considered as known trends, in an expressive manner. Detrended methods are suitable for characterizing the artistic…
Some of the theoretical motivations and experimental developments leading to the discovery of charm are recalled.
In this paper, we propose a novel generalisation of the signature of a path, motivated by fractional calculus, which is able to describe the solutions of linear Caputo controlled FDEs. We also propose another generalisation of the…