Fractals In Music

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Fractals In Music

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Author : Charles B. Madden
language : en
Publisher: High Art Press
Release Date : 1999

Fractals In Music written by Charles B. Madden and has been published by High Art Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Fractals in Music is intended for advanced students of music theory, whether individuals, composers, students, or teachers. It is intelligible to anyone having some knowledge of algebra and trigonometry. The many illustrations clarify such concepts as self-similarity and transforms. Book jacket.

Music And Mathematics

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Author : John Fauvel
language : en
Publisher: Oxford University Press, USA
Release Date : 2003

Music And Mathematics written by John Fauvel and has been published by Oxford University Press, USA this book supported file pdf, txt, epub, kindle and other format this book has been release on 2003 with Mathematics categories.

From ancient Greek times, music has been seen as a mathematical art, and the relationship between mathematics and music has fascinated generations. This work links these two subjects in a manner that is suitable for students of both subjects, as well as the general reader with an interest in music.

Fractal Music Hypercards And More

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Author : Martin Gardner
language : en
Publisher:
Release Date : 1978

Fractal Music Hypercards And More written by Martin Gardner and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1978 with Mathematical recreations categories.

Fractals In Science

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Author : Armin Bunde
language : en
Publisher: Springer
Release Date : 2013-12-21

Fractals In Science written by Armin Bunde and has been published by Springer this book supported file pdf, txt, epub, kindle and other format this book has been release on 2013-12-21 with Science categories.

Applying fractal geometry to science is bringing about a breakthrough in our understanding of complex systems in nature that show self-similar or self-affine features. Self-similar and self-affine processes appear everywhere in nature, in galaxies and landscapes, in earthquakes and geological cracks, in aggregates and colloids, in rough surfaces and interfaces, in glassy materials and polymers, in proteins as well as in other large molecules. Fractal structures appear also in the human body; well known examples include the lung and the vascular system. Furthermore, fractal geometry is an important tool in the analysis of phenomena as diverse as rhythms in music melodies and in the human heart beat and DNA sequences. Since the pioneering work of B.B. Mandelbrot, this interdisciplinary field has expanded very rapidly. The scientific community applying fractal concepts is very broad and ranges from astronomers, geoscientists, physicists, chemists and engineers to biologists and those engaging in medical research.

Fractals Graphics And Mathematics Education

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Author : Michael Frame
language : en
Publisher: Cambridge University Press
Release Date : 2002-06-20

Fractals Graphics And Mathematics Education written by Michael Frame and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2002-06-20 with Computers categories.

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Making Music With Computers

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Author : Bill Manaris
language : en
Publisher: CRC Press
Release Date : 2014-05-19

Making Music With Computers written by Bill Manaris and has been published by CRC Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 2014-05-19 with Computers categories.

Teach Your Students How to Use Computing to Explore Powerful and Creative IdeasIn the twenty-first century, computers have become indispensable in music making, distribution, performance, and consumption. Making Music with Computers: Creative Programming in Python introduces important concepts and skills necessary to generate music with computers.

Fractals And Chaos In Geology And Geophysics

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Author : Donald L. Turcotte
language : en
Publisher: Cambridge University Press
Release Date : 1997-07-13

Fractals And Chaos In Geology And Geophysics written by Donald L. Turcotte and has been published by Cambridge University Press this book supported file pdf, txt, epub, kindle and other format this book has been release on 1997-07-13 with Mathematics categories.

The fundamental concepts of fractal geometry and chaotic dynamics, along with the related concepts of multifractals, self-similar time series, wavelets, and self-organized criticality, are introduced in this book, for a broad range of readers interested in complex natural phenomena. Now in a greatly expanded, second edition, this book relates fractals and chaos to a variety of geological and geophysical applications. All concepts are introduced at the lowest possible level of mathematics consistent with their understanding, so that the reader requires only a background in basic physics and mathematics.

The Geometry Of Fractals A New Perspective

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Author : Pasquale De Marco
language : en
Publisher: Pasquale De Marco
Release Date : 2025-07-07

The Geometry Of Fractals A New Perspective written by Pasquale De Marco and has been published by Pasquale De Marco this book supported file pdf, txt, epub, kindle and other format this book has been release on 2025-07-07 with Science categories.

Embark on a captivating journey into the realm of fractals, where intricate patterns and self-similarity unveil the hidden beauty and complexity of the natural world. This comprehensive guide delves into the mathematical foundations, applications, and cultural significance of fractals, offering a fresh perspective on these fascinating geometric structures. From the delicate branching of snowflakes to the mesmerizing spirals of seashells, fractals are found in abundance in nature, revealing a level of order within apparent chaos. Botanists, geologists, and meteorologists alike have discovered the fractal patterns that govern the growth of plants, the formation of mountains, and the behavior of clouds. This book takes you on an exploration of the history of fractals, tracing their origins from early mathematical investigations to the groundbreaking work of Benoit Mandelbrot, who brought fractals to the forefront of scientific study. Discover the mathematical concepts that underlie fractal geometry, including set theory, topology, and measure theory. Beyond their mathematical elegance, fractals have found practical applications in diverse fields. Computer scientists utilize fractals to generate realistic images and animations, while engineers harness their properties for signal processing and data compression. Fractals have also inspired new forms of art and music, captivating audiences with their intricate patterns and dynamic forms. This book is not just a scientific treatise; it is an invitation to appreciate the beauty and wonder of fractals. Whether you are a mathematician, a scientist, an artist, or simply someone curious about the world around you, you will find something to engage and inspire you within these pages. **Unveil the Secrets of Fractals:** * Explore the mathematical underpinnings of fractal geometry, including set theory, topology, and measure theory. * Delve into the history of fractals, from early investigations to the groundbreaking work of Benoit Mandelbrot. * Discover the diverse applications of fractals in fields such as computer graphics, image processing, and signal processing. * Appreciate the cultural significance of fractals in art, music, and literature. * Gain a deeper understanding of the beauty and complexity of the natural world through the lens of fractals. If you like this book, write a review on google books!

African Fractals

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Author : Ron Eglash
language : en
Publisher:
Release Date : 1999

African Fractals written by Ron Eglash and has been published by this book supported file pdf, txt, epub, kindle and other format this book has been release on 1999 with Mathematics categories.

Fractals are characterized by the repetition of similar patterns at ever-diminishing scales. Fractal geometry has emerged as one of the most exciting frontiers on the border between mathematics and information technology and can be seen in many of the swirling patterns produced by computer graphics. It has become a new tool for modeling in biology, geology, and other natural sciences. Anthropologists have observed that the patterns produced in different cultures can be characterized by specific design themes. In Europe and America, we often see cities laid out in a grid pattern of straight streets and right-angle corners. In contrast, traditional African settlements tend to use fractal structures-circles of circles of circular dwellings, rectangular walls enclosing ever-smaller rectangles, and streets in which broad avenues branch down to tiny footpaths with striking geometric repetition. These indigenous fractals are not limited to architecture; their recursive patterns echo throughout many disparate African designs and knowledge systems. Drawing on interviews with African designers, artists, and scientists, Ron Eglash investigates fractals in African architecture, traditional hairstyling, textiles, sculpture, painting, carving, metalwork, religion, games, practical craft, quantitative techniques, and symbolic systems. He also examines the political and social implications of the existence of African fractal geometry. His book makes a unique contribution to the study of mathematics, African culture, anthropology, and computer simulations.