A Tale Of Two Fractals
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A Tale of Two Fractals
Author: A.A. Kirillov
language: en
Publisher: Springer Science & Business Media
Release Date: 2013-04-23
Since Benoit Mandelbrot's pioneering work in the late 1970s, scores of research articles and books have been published on the topic of fractals. Despite the volume of literature in the field, the general level of theoretical understanding has remained low; most work is aimed either at too mainstream an audience to achieve any depth or at too specialized a community to achieve widespread use. Written by celebrated mathematician and educator A.A. Kirillov, A Tale of Two Fractals is intended to help bridge this gap, providing an original treatment of fractals that is at once accessible to beginners and sufficiently rigorous for serious mathematicians. The work is designed to give young, non-specialist mathematicians a solid foundation in the theory of fractals, and, in the process, to equip them with exposure to a variety of geometric, analytical, and algebraic tools with applications across other areas.
Russian Fractals in Indigenous Artifacts
This book is the first comprehensive work on Russian Fractals in indigenous artifacts. While existing works focus on universal phenomena, such as liquid crystal or finance, none explore the intersection between Fractals and Russia. 'Russian Fractals in Indigenous Artifacts' therefore investigates how indigenous Russian cultures have a wonderful Fractal heritage that was originally tied to socially just and ecologically sustainable social practices, including those of indigenous northern groups such as the Yakut. Fractal designs originally allowed unalienated value, both human and nonhuman, to be visible, thereby enabling just and sustainable living. This book also examines how the tsarist elite encouraged the creation of unique creative masterpieces, developing and strengthening traditional crafts and art of indigenous people—hence, Fabergé, or imperial architecture. Today, the challenge for contemporary Russia is to reestablish the relationship between the social and ecological sustainability of indigenous cultures and practices, for which we can now provide modeling and analysis. Lay attempts at this have only limited success, as they have based the attempts on a purely religious basis, which recognizes the ecological aspects but often succumbs to authoritarian nationalism. However, the freely accession of indigenous peoples to Russia for the sake of national liberation has had a positive effect on enriching them with spirituality and creativity by Fractal artifacts through friendly exchanges with one another. In 'Russian Fractals in Indigenous Artifacts,' Bangura and Zhigun express why there is a need for a forward-thinking Fractal renaissance in Russia, bringing together contemporary computational and scientific analyses with these ecologically and socially sustainable traditions.
The Butterfly in the Quantum World
Author: Indubala I Satija
language: en
Publisher: Morgan & Claypool Publishers
Release Date: 2016-09-06
Butterfly in the Quantum World by Indu Satija, with contributions by Douglas Hofstadter, is the first book ever to tell the story of the "Hofstadter butterfly", a beautiful and fascinating graph lying at the heart of the quantum theory of matter. The butterfly came out of a simple-sounding question: What happens if you immerse a crystal in a magnetic field? What energies can the electrons take on? From 1930 onwards, physicists struggled to answer this question, until 1974, when graduate student Douglas Hofstadter discovered that the answer was a graph consisting of nothing but copies of itself nested down infinitely many times. This wild mathematical object caught the physics world totally by surprise, and it continues to mesmerize physicists and mathematicians today. The butterfly plot is intimately related to many other important phenomena in number theory and physics, including Apollonian gaskets, the Foucault pendulum, quasicrystals, the quantum Hall effect, and many more. Its story reflects the magic, the mystery, and the simplicity of the laws of nature, and Indu Satija, in a wonderfully personal style, relates this story, enriching it with a vast number of lively historical anecdotes, many photographs, beautiful visual images, and even poems, making her book a great feast, for the eyes, for the mind and for the soul.