1. Getting Acquainted With Fractals
by Helmberg, Gilbert 
Price: USD 13.61
Dealer: Alibris, ThriftBooks-Dallas via Alibris
Description: de Gruyter 2007 Hardcover Good Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less. 

2. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 16.08
Dealer: Abebooks, ThriftBooks-Atlanta
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: de Gruyter] Hardcover Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less 0.98 [AUSTELL, GA, U.S.A.] [Publication Year: 2007]  

3. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 16.47
Dealer: ZVAB, medimops
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover Gut/Very good: Buch bzw. Schutzumschlag mit wenigen Gebrauchsspuren an Einband, Schutzumschlag oder Seiten. / Describes a book or dust jacket that does show some signs of wear on either the binding, dust jacket or pages. [Berlin, Germany] [Publication Year: 2007]  

4. Getting Acquainted with Fractals
by Helmberg Gilbert 
Price: USD 17.61
Dealer: Biblio, ThriftBooks
Description: de Gruyter, Date: 2007. Hardcover. Good. Pages can have notes/highlighting. Spine may show signs of wear. ~ ThriftBooks: Read More, Spend Less.Dust jacket quality is not guaranteed. 2007. de Gruyter ISBN 3110190923 9783110190922 [US] 

5. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 18.14
Dealer: AbebooksDE, medimops
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover Gut/Very good: Buch bzw. Schutzumschlag mit wenigen Gebrauchsspuren an Einband, Schutzumschlag oder Seiten. / Describes a book or dust jacket that does show some signs of wear on either the binding, dust jacket or pages. [Berlin, Germany] [Publication Year: 2007]  

6. Getting Acquainted With Fractals
by Gilbert Helmberg 
Price: USD 22.89
Dealer: Biblio, Ergodebooks
Description: Walter de Gruyter, Date: 2007-03-01. Hardcover. Good. 2007. Walter de Gruyter ISBN 3110190923 9783110190922 [US] 

7. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 171.10
Dealer: Abebooks, GoldenWavesOfBooks
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover New. Fast Shipping and good customer service [Fayetteville, TX, U.S.A.] [Publication Year: 2007]  

8. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 171.82
Dealer: Abebooks, GoldBooks
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover New Copy. Customer Service Guaranteed [Denver, CO, U.S.A.] [Publication Year: 2007]  

9. Getting Acquainted with Fractals
by Gilbert Helmberg 
Price: USD 174.05
Dealer: ZVAB, AHA-BUCH GmbH
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover Druck auf Anfrage Neuware - Printed after ordering - 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 doing that until the result is greater than some number. The number of times you have to run the equations to get out of an 'orbit' not specified here can be assigned a colour and then the pixel (x,y) gets turned that colour, unless those coordinates can't get out of their orbit, in which case they are made black. Later it was Benoit Mandelbrot who used computers to produce fractals. A basic property of fractals is that they contain a large degree of self similarity, i.e., they usually contain little copies within the original, and these copies also have infinite detail. That means the more you zoom in on a fractal, the more detail you get, and this keeps going on forever and ever. The well-written book 'Getting acquainted with fractals' by Gilbert Helmberg provides a mathematically oriented introduction to fractals, with a focus upon three types of fractals: fractals of curves, attractors for iterative function systems in the plane, and Julia sets. The presentation is on an undergraduate level, with an ample presentation of the corresponding mathematical background, e.g., linear algebra, calculus, algebra, geometry, topology, measure theory and complex analysis. The book contains over 170 color illustrations. [Einbeck, Germany] [Publication Year: 2007]  

10. Getting Acquainted with Fractals
by Gilbert Helmberg 
Price: USD 191.78
Dealer: AbebooksDE, AHA-BUCH GmbH
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover Druck auf Anfrage Neuware - Printed after ordering - 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 doing that until the result is greater than some number. The number of times you have to run the equations to get out of an 'orbit' not specified here can be assigned a colour and then the pixel (x,y) gets turned that colour, unless those coordinates can't get out of their orbit, in which case they are made black. Later it was Benoit Mandelbrot who used computers to produce fractals. A basic property of fractals is that they contain a large degree of self similarity, i.e., they usually contain little copies within the original, and these copies also have infinite detail. That means the more you zoom in on a fractal, the more detail you get, and this keeps going on forever and ever. The well-written book 'Getting acquainted with fractals' by Gilbert Helmberg provides a mathematically oriented introduction to fractals, with a focus upon three types of fractals: fractals of curves, attractors for iterative function systems in the plane, and Julia sets. The presentation is on an undergraduate level, with an ample presentation of the corresponding mathematical background, e.g., linear algebra, calculus, algebra, geometry, topology, measure theory and complex analysis. The book contains over 170 color illustrations. [Einbeck, Germany] [Publication Year: 2007]  

11. Getting Acquainted with Fractals
by Gilbert Helmberg 
Price: USD 199.34
Dealer: Biblio, Ria Christie Collections
Description: Hard Cover. New. New Book; Fast Shipping from UK; Not signed; Not First Edition; The Getting Acquainted with Fractals. ISBN 3110190923 9783110190922 [GB] 

12. Getting Acquainted With Fractals
by Gilbert Helmberg 
Price: USD 201.26
Dealer: Alibris, Books2anywhere via Alibris
Description: De Gruyter 3/19/2007 12: 00: 00 AM Hardcover PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK. 

13. Getting Acquainted With Fractals
by Gilbert Helmberg 
Price: USD 212.36
Dealer: Alibris, Paperbackshop International via Alibris
Description: De Gruyter 3/19/2007 12: 00: 00 AM Hardcover PLEASE NOTE, WE DO NOT SHIP TO DENMARK. New Book. Shipped from UK in 4 to 14 days. Established seller since 2000. Please note we cannot offer an expedited shipping service from the UK. 

14. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 218.46
Dealer: Alibris, Ria Christie Books via Alibris
Description: Berlin/Boston de Gruyter 2007 Hard cover New. Sewn binding. Paper over boards. 177 p. Contains: Illustrations, black & white, Illustrations, color, Figures. 

15. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 241.56
Dealer: Alibris
Description: Berlin/Boston de Gruyter 2007 Hard cover New. Sewn binding. Paper over boards. 177 p. Contains: Illustrations, black & white, Illustrations, color, Figures. 

16. Getting Acquainted With Fractals
by Helmberg Gilbert 
Price: USD 251.76
Dealer: Biblio, Revaluation Books
Description: Walter De Gruyter Inc, Date: 2007. Paperback. New. illustrated edition. 177 pages. 9.50x6.75x0.50 inches. 2007. Walter De Gruyter Inc ISBN 3110190923 9783110190922 [GB] 

17. Getting Acquainted With Fractals
by Helmberg, Gilbert 
Price: USD 254.13
Dealer: Alibris, Revaluation Books via Alibris
Description: Walter De Gruyter Inc 2007 Softcover New Illustrated edition. 177 pages. 9.50x6.75x0.50 inches. 

18. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 264.47
Dealer: Abebooks, Lucky's Textbooks
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover [Dallas, TX, U.S.A.] [Publication Year: 2007]  

19. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 339.49
Dealer: Abebooks, Kennys Bookshop and Art Galleries Ltd.
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover [Galway, GY, Ireland] [Publication Year: 2007]  

20. Getting Acquainted with Fractals
by Helmberg, Gilbert 
Price: USD 416.49
Dealer: Abebooks, Kennys Bookstore
Description: ISBN10: 3110190923, ISBN13: 9783110190922, [publisher: De Gruyter] Softcover [Olney, MD, U.S.A.] [Publication Year: 2007]