LEADER 03977nam 2200709Ia 450 001 9910454645903321 005 20211128145400.0 010 $a1-282-19665-0 010 $a9786612196652 010 $a3-11-020661-7 024 7 $a10.1515/9783110190922 035 $a(CKB)1000000000698106 035 $a(EBL)453861 035 $a(OCoLC)471131227 035 $a(SSID)ssj0000162582 035 $a(PQKBManifestationID)11167070 035 $a(PQKBTitleCode)TC0000162582 035 $a(PQKBWorkID)10208015 035 $a(PQKB)10296266 035 $a(MiAaPQ)EBC453861 035 $a(DE-B1597)34315 035 $a(OCoLC)1013937560 035 $a(OCoLC)853244006 035 $a(DE-B1597)9783110206616 035 $a(PPN)17552050X$9sudoc 035 $a(PPN)140849130 035 $a(Au-PeEL)EBL453861 035 $a(CaPaEBR)ebr10317956 035 $a(CaONFJC)MIL219665 035 $a(OCoLC)935268925 035 $a(EXLCZ)991000000000698106 100 $a20061215d2007 uy 0 101 0 $aeng 135 $aur||#|||||||| 181 $ctxt 182 $cc 183 $acr 200 10$aGetting acquainted with fractals$b[electronic resource] /$fby Gilbert Helmberg 210 $aBerlin ;$aNew York $cWalter de Gruyter$d2007 215 $a1 online resource (188 p.) 300 $aDescription based upon print version of record. 311 $a3-11-019092-3 320 $aIncludes bibliographical references. 327 $tFrontmatter --$tContents --$tFractals and dimension --$tIterative function systems --$tIteration of complex polynomials --$tBibliography --$tList of symbols --$tIndex --$tContents (detailed) 330 $aThe 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. 606 $aFractals 606 $aGeometry 608 $aElectronic books. 610 $aFractals. 610 $ameasure theory. 615 0$aFractals. 615 0$aGeometry. 676 $a514/.742 686 $aSK 380$2rvk 700 $aHelmberg$b Gilbert$047649 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a9910454645903321 996 $aGetting acquainted with fractals$92472084 997 $aUNINA