



LEADER 
03199nam a2200397 u 4500 
001 
EB001887609 
003 
EBX01000000000000001050970 
005 
00000000000000.0 
007 
tu 
008 
191222 r  eng 
020 


a 9783110206616

050 

4 
a QA614.86

100 
1 

a Helmberg, Gilbert

245 
0 
0 
a Getting Acquainted with Fractals
h Elektronische Ressource
c Gilbert Helmberg

260 


a Berlin
b De Gruyter
c 2008, [2008]©2007

300 


a 1 online resource

653 


a Frakta

653 


a Maßtheorie

653 


a Fraktal

041 
0 
7 
a eng
2 ISO 6392

989 


b GRUYMPG
a DeGruyter MPG Collection

500 


a Mode of access: Internet via World Wide Web

028 
5 
0 
a 10.1515/9783110190922

773 
0 

t DGBA Backlist Mathematics English Language 20002014

773 
0 

t DGBA Backlist Complete English Language 20002014 PART1

773 
0 

t EBOOK PACKAGE ENGLISH LANGUAGES TITLES 2008

773 
0 

t DGBA Mathematics 2000  2014

773 
0 

t EBOOK PAKET SCIENCE TECHNOLOGY AND MEDICINE 2008

773 
0 

t EBOOK GESAMTPAKET / COMPLETE PACKAGE 2008

856 
4 
0 
u https://www.degruyter.com/document/doi/10.1515/9783110206616/html
x Verlag
3 Volltext

082 
0 

a 514.742

650 

4 
a measure theory

650 

4 
a MATHEMATICS / Topology / bisacsh

650 

4 
a Geometry

650 

4 
a Fractals

520 


a The first instance of precomputer 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 wellwritten 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
