Getting acquainted with fractals:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Elektronisch E-Book |
| Sprache: | English |
| Veröffentlicht: |
Berlin
Walter de Gruyter
2007
|
| Schlagworte: | |
| Online-Zugang: | FAW01 FAW02 Volltext |
| Beschreibung: | Includes bibliographical references The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doi FRACTALS AND DIMENSIONS: The game of deleting and replacing -- The box-counting dimension -- The Hausdorff dimension -- ITERATIVE FUNCTION SYSTEMS: The space of compact subsets of a complete metric space -- Contractions in a complete metric space -- Affine iterative functions in R² -- ITERATION OF COMPLEX POLYNOMIALS: General theory of Julia sets -- Julia sets for quadratic polynomials -- The Mandelbrot set -- Generation of Julia sets |
| Beschreibung: | 1 Online-Ressource (177 pages) |
| ISBN: | 1282196650 3110206617 9781282196650 9783110206616 |
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| 500 | |a The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doi | ||
| 500 | |a FRACTALS AND DIMENSIONS: The game of deleting and replacing -- The box-counting dimension -- The Hausdorff dimension -- ITERATIVE FUNCTION SYSTEMS: The space of compact subsets of a complete metric space -- Contractions in a complete metric space -- Affine iterative functions in R² -- ITERATION OF COMPLEX POLYNOMIALS: General theory of Julia sets -- Julia sets for quadratic polynomials -- The Mandelbrot set -- Generation of Julia sets | ||
| 650 | 7 | |a MATHEMATICS / Topology |2 bisacsh | |
| 650 | 7 | |a Fractals |2 fast | |
| 650 | 7 | |a Geometry |2 fast | |
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| author | Helmberg, Gilbert |
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| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 514 - Topology |
| dewey-raw | 514/.742 |
| dewey-search | 514/.742 |
| dewey-sort | 3514 3742 |
| dewey-tens | 510 - Mathematics |
| discipline | Mathematik |
| format | Electronic eBook |
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| spelling | Helmberg, Gilbert Verfasser aut Getting acquainted with fractals by Gilbert Helmberg Berlin Walter de Gruyter 2007 1 Online-Ressource (177 pages) txt rdacontent c rdamedia cr rdacarrier Includes bibliographical references The first instance of pre-computer fractals was noted by the French mathematician Gaston Julia. He wondered what a complex polynomial function would look like, such as the ones named after him (in the form of z2 + c, where c is a complex constant with real and imaginary parts). The idea behind this formula is that one takes the x and y coordinates of a point z, and plug them into z in the form of x + i*y, where i is the square root of -1, square this number, and then add c, a constant. Then plug the resulting pair of real and imaginary numbers back into z, run the operation again, and keep doi FRACTALS AND DIMENSIONS: The game of deleting and replacing -- The box-counting dimension -- The Hausdorff dimension -- ITERATIVE FUNCTION SYSTEMS: The space of compact subsets of a complete metric space -- Contractions in a complete metric space -- Affine iterative functions in R² -- ITERATION OF COMPLEX POLYNOMIALS: General theory of Julia sets -- Julia sets for quadratic polynomials -- The Mandelbrot set -- Generation of Julia sets MATHEMATICS / Topology bisacsh Fractals fast Geometry fast Fraktal swd Fractals Geometry Fraktal (DE-588)4123220-3 gnd rswk-swf Fraktal (DE-588)4123220-3 s 1\p DE-604 Erscheint auch als Druckausgabe 978-3-11-019092-2 http://search.ebscohost.com/login.aspx?direct=true&scope=site&db=nlebk&db=nlabk&AN=281608 Aggregator Volltext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Helmberg, Gilbert Getting acquainted with fractals MATHEMATICS / Topology bisacsh Fractals fast Geometry fast Fraktal swd Fractals Geometry Fraktal (DE-588)4123220-3 gnd |
| subject_GND | (DE-588)4123220-3 |
| title | Getting acquainted with fractals |
| title_auth | Getting acquainted with fractals |
| title_exact_search | Getting acquainted with fractals |
| title_full | Getting acquainted with fractals by Gilbert Helmberg |
| title_fullStr | Getting acquainted with fractals by Gilbert Helmberg |
| title_full_unstemmed | Getting acquainted with fractals by Gilbert Helmberg |
| title_short | Getting acquainted with fractals |
| title_sort | getting acquainted with fractals |
| topic | MATHEMATICS / Topology bisacsh Fractals fast Geometry fast Fraktal swd Fractals Geometry Fraktal (DE-588)4123220-3 gnd |
| topic_facet | MATHEMATICS / Topology Fractals Geometry Fraktal |
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