Related papers: "Fractal Expression" in Chinese Calligraphy
Can you stretch and reform a curve such that it fills a square completely? This question dates back to 18th century, the origin of space-filling curves. It was proved affirmatively by many great mathematicians. In this document, we…
As one type of incidence theory, the geometry of pentagram map seems quite classical at first. However, this is an excellent example of such a classical idea developed into a marvellous insight by some modern approach. We introduce an…
Chinese is one of the most widely used languages in the world, yet online handwritten Chinese character recognition (OLHCCR) remains challenging. To recognize Chinese characters, one popular choice is to adopt the 2D convolutional neural…
As a streak of dye is advected by a chaotic flow, it stretches and folds and becomes indistinguishable from a one-dimensional idealized material line. The variation along a material line of the total stretching experienced by fluid elements…
Topological properties of crystals and quasicrystals is a subject of recent and growing interest. This Letter reports an experiment where, for certain quasicrystals, these properties can be directly retrieved from diffraction. We directly…
A class of simplified measures is constructed to capture the key features of generic spatio-temporally chaotic systems. A combined analytical and numerical investigation allows us to extablish the scaling beahviour of the fractal dimension…
Starting with a substitution tiling, we demonstrate a method for constructing infinitely many new substitution tilings. Each of these new tilings is derived from a graph iterated function system and the tiles have fractal boundary. We show…
The Chinese Roots of Linear Algebra by Roger Hart chronicles the linear problems of ancient China in the Nine Chapters of the Mathematical Art, and supplies new insights about their solution.
It was demonstrated that there is a geometrical order in the structure of literature. Fractal geometry as a modern mathematical approach and a new geometrical viewpoint on natural objects including both processes and structures was employed…
We have built a new kind of manifolds which leads to an alternative new geometrical space. The study of the nowhere differentiable functions via a family of mean functions leads to a new characterization of this category of functions. A…
We report the first observation of the periodical properties for Talbot effect with {\pi} phase jump. Analytical expressions are derived from simplified modal method to analyze the novelty phenomenon of the Talbot effect with {\pi} phase…
We investigate the contentions that Jackson Pollock's drip paintings are fractals produced by the artist's Levy distributed motion and that fractal analysis may be used to authenticate works of uncertain provenance[1-5]. We find that the…
Motivated by children inventing creatively laws on how to add or multiply fractions, we introduce four fraction operations and discover some of their properties.
The possible discovery of astronomical effects due to precession - such as the shift in the declination of heliacal raising of bright stars or the precession of the equinoxes - is reviewed for various ancient cultures in the world. Although…
Dictionary learning is a cornerstone of image classification. We set out to address a longstanding challenge in using dictionary learning for classification; that is to simultaneously maximise the discriminability and…
An expression for four-tangle is obtained by examining the negativity fonts present in a four-way partial transpose under local unitary operations. An alternate derivation of three tangle is also given.
To travel into the past, to observe it, perhaps to influence it and correct mistakes of one's youth, has been an abiding fantasy of mankind for as long as we have been aware of a past. Here are described some recent scientific…
This work is an analytical and numerical study of the composition of several fractals into one and of the relation between the composite dimension and the dimensions of the component fractals. In the case of composition of standard IFS with…
The present work proposes the development of a novel method to provide descriptors for colored texture images. The method consists in two steps. In the first, we apply a linear transform in the color space of the image aiming at…
Handwriting recognition is of crucial importance to both Human Computer Interaction (HCI) and paperwork digitization. In the general field of Optical Character Recognition (OCR), handwritten Chinese character recognition faces tremendous…