Fractalize that!: a visual essay on statistical geometry
"Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski...
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Singapore
World Scientific Publishing Company Pte Limited
2019
|
| Schlagworte: | |
| Online-Zugang: | UBY01 Volltext |
| Zusammenfassung: | "Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers. The algorithm claims to be universal in scope, in that it can fill any spatial region with smaller and smaller fill regions of any shape. The filling is complete in the limit of an infinite number of fill regions. This book presents a descriptive development of the subject using the traditional shapes of geometry such as discs, squares, and triangles. It contains a detailed mathematical treatment of all that is currently known about the algorithm, as well as a chapter on software implementation of the algorithm. The mathematician will find a wealth of interesting conjectures supported by numerical computation. Physicists are offered a model looking for an application. The patterns generated are often quite interesting as abstract art. Readers can also create these computer-generated art with the advice and examples provided."-- |
| Beschreibung: | Introduction : space-filling patterns -- Squares and rectangles -- Triangles and diamonds -- Discs and circular arcs -- Mixed and irregular shapes -- Mixed and irregular shapes -- Examples -- The statistical geometry algorithm -- The area-perimeter algorithm -- Statistical geometry in one dimension -- Do it yourself. - Includes bibliographical references |
| Beschreibung: | 1 online resource (124 pages) illustrations |
| ISBN: | 9789813275171 |
Internformat
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| 500 | |a Introduction : space-filling patterns -- Squares and rectangles -- Triangles and diamonds -- Discs and circular arcs -- Mixed and irregular shapes -- Mixed and irregular shapes -- Examples -- The statistical geometry algorithm -- The area-perimeter algorithm -- Statistical geometry in one dimension -- Do it yourself. - Includes bibliographical references | ||
| 520 | |a "Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers. The algorithm claims to be universal in scope, in that it can fill any spatial region with smaller and smaller fill regions of any shape. The filling is complete in the limit of an infinite number of fill regions. This book presents a descriptive development of the subject using the traditional shapes of geometry such as discs, squares, and triangles. It contains a detailed mathematical treatment of all that is currently known about the algorithm, as well as a chapter on software implementation of the algorithm. The mathematician will find a wealth of interesting conjectures supported by numerical computation. Physicists are offered a model looking for an application. The patterns generated are often quite interesting as abstract art. Readers can also create these computer-generated art with the advice and examples provided."-- | ||
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Datensatz im Suchindex
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| author | Shier, John (Writer on geometry) |
| author_facet | Shier, John (Writer on geometry) |
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| author_sort | Shier, John (Writer on geometry) |
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| bvnumber | BV046810904 |
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| dewey-full | 516/.132 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 516 - Geometry |
| dewey-raw | 516/.132 |
| dewey-search | 516/.132 |
| dewey-sort | 3516 3132 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| discipline_str_mv | Mathematik |
| format | Electronic eBook |
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| id | DE-604.BV046810904 |
| illustrated | Illustrated |
| index_date | 2024-07-03T14:58:51Z |
| indexdate | 2024-07-10T08:54:29Z |
| institution | BVB |
| isbn | 9789813275171 |
| language | English |
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| physical | 1 online resource (124 pages) illustrations |
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| spelling | Shier, John (Writer on geometry) aut Fractalize that! a visual essay on statistical geometry by John Shier Singapore World Scientific Publishing Company Pte Limited 2019 1 online resource (124 pages) illustrations txt rdacontent c rdamedia cr rdacarrier Introduction : space-filling patterns -- Squares and rectangles -- Triangles and diamonds -- Discs and circular arcs -- Mixed and irregular shapes -- Mixed and irregular shapes -- Examples -- The statistical geometry algorithm -- The area-perimeter algorithm -- Statistical geometry in one dimension -- Do it yourself. - Includes bibliographical references "Fractalize That! A Visual Essay on Statistical Geometry brings a new class of geometric fractals to a wider audience of mathematicians and scientists. It describes a recently discovered random fractal space-filling algorithm. Connections with tessellations and known fractals such as Sierpinski are developed. And, the mathematical development is illustrated by a large number of colorful images that will charm the readers. The algorithm claims to be universal in scope, in that it can fill any spatial region with smaller and smaller fill regions of any shape. The filling is complete in the limit of an infinite number of fill regions. This book presents a descriptive development of the subject using the traditional shapes of geometry such as discs, squares, and triangles. It contains a detailed mathematical treatment of all that is currently known about the algorithm, as well as a chapter on software implementation of the algorithm. The mathematician will find a wealth of interesting conjectures supported by numerical computation. Physicists are offered a model looking for an application. The patterns generated are often quite interesting as abstract art. Readers can also create these computer-generated art with the advice and examples provided."-- Tessellations (Mathematics) Fractals Algebraic spaces Geometry, Algebraic Electronic books Geometrie (DE-588)4020236-7 gnd rswk-swf Fraktal (DE-588)4123220-3 gnd rswk-swf Stochastische Geometrie (DE-588)4133202-7 gnd rswk-swf Statistik (DE-588)4056995-0 gnd rswk-swf Fraktal (DE-588)4123220-3 s Geometrie (DE-588)4020236-7 s Statistik (DE-588)4056995-0 s DE-604 Stochastische Geometrie (DE-588)4133202-7 s Erscheint auch als Druck-Ausgabe 9789813275164 https://www.worldscientific.com/worldscibooks/10.1142/11126 Verlag URL des Erstveröffentlichers Volltext |
| spellingShingle | Shier, John (Writer on geometry) Fractalize that! a visual essay on statistical geometry Tessellations (Mathematics) Fractals Algebraic spaces Geometry, Algebraic Electronic books Geometrie (DE-588)4020236-7 gnd Fraktal (DE-588)4123220-3 gnd Stochastische Geometrie (DE-588)4133202-7 gnd Statistik (DE-588)4056995-0 gnd |
| subject_GND | (DE-588)4020236-7 (DE-588)4123220-3 (DE-588)4133202-7 (DE-588)4056995-0 |
| title | Fractalize that! a visual essay on statistical geometry |
| title_auth | Fractalize that! a visual essay on statistical geometry |
| title_exact_search | Fractalize that! a visual essay on statistical geometry |
| title_exact_search_txtP | Fractalize that! a visual essay on statistical geometry |
| title_full | Fractalize that! a visual essay on statistical geometry by John Shier |
| title_fullStr | Fractalize that! a visual essay on statistical geometry by John Shier |
| title_full_unstemmed | Fractalize that! a visual essay on statistical geometry by John Shier |
| title_short | Fractalize that! |
| title_sort | fractalize that a visual essay on statistical geometry |
| title_sub | a visual essay on statistical geometry |
| topic | Tessellations (Mathematics) Fractals Algebraic spaces Geometry, Algebraic Electronic books Geometrie (DE-588)4020236-7 gnd Fraktal (DE-588)4123220-3 gnd Stochastische Geometrie (DE-588)4133202-7 gnd Statistik (DE-588)4056995-0 gnd |
| topic_facet | Tessellations (Mathematics) Fractals Algebraic spaces Geometry, Algebraic Electronic books Geometrie Fraktal Stochastische Geometrie Statistik |
| url | https://www.worldscientific.com/worldscibooks/10.1142/11126 |
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