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 LEADER 03794nam 2200613 450 001 996440647603316 005 20200520144314.0 010 $a3-11-052683-2 010 $a3-11-052952-1 024 7 $a10.1515/9783110529524 035 $a(CKB)4340000000203619 035 $a(MiAaPQ)EBC5049511 035 $a(DE-B1597)474833 035 $a(OCoLC)1004871969 035 $a(DE-B1597)9783110529524 035 $a(Au-PeEL)EBL5049511 035 $a(CaPaEBR)ebr11443158 035 $a(OCoLC)1004623923 035 $a(EXLCZ)994340000000203619 100 $a20171025h20172017 uy 0 101 0 $ager 135 $aurcnu|||||||| 181 $2rdacontent 182 $2rdamedia 183 $2rdacarrier 200 00$aVorsorgen in der Moderne /$fHerausgegeben von Nicolai Hannig und Malte Thiessen 210 1$aBerlin, [Germany] ;$aBoston, [Massachusetts] :$cDe Gruyter Oldenbourg,$d2017. 210 4$d©2017 215 $a1 online resource (260 pages) $cillustrations 225 1 $aSchriftenreihe der Vierteljahrshefte fur Zeitgeschichte ;$vBand 115 300 $aIncludes index. 311 $a3-11-052677-8 327 $tFrontmatter -- $tInhalt -- $tVorsorge und Prävention in der Moderne -- $tHumanitäre Intervention und Prävention in der internationalen Politik vom 19. bis ins 21. Jahrhundert -- $tLebenslang. Sozialprognose und Kriminalprävention, 1890?1980 -- $tIm Fahrwasser der Finanzmärkte -- $tDas Zeitalter der Ungewissheit: Zukunftsszenarien und globale Bedrohung nach dem Zweiten Weltkrieg -- $t?Menschliches Versagen? in der Kernenergie -- $tWirtschaftspolitik für eine unbestimmte Zukunft -- $tAutomatismen als Unfallprävention? -- $tSorglosigkeit und Versicherheitlichung -- $tVorsorgen oder Ausbrennen -- $t?Nature always counts?. Kalorienzählen als Vorsorgetechnik in den USA des frühen 20. Jahrhunderts -- $tVorsorge als Zukunftshandeln -- $tDank -- $tAbkürzungen -- $tDie Autorinnen und Autoren dieses Bandes -- $tPersonenregister 330 $aThe volume traces the history of the social phenomenon of "provisioning for the future" in politics, technology, economics, and private life in the 20th century, illuminating its determinants and consequences. It covers providers and beneficiaries, proponents and opponents, profiteers and victims. This social history of Vorsorge, at once multi-faceted and well-documented, provides new insight into the transformation of modern societies. 330 $aVorsorge ist überall. Als Gesundheits-, Kriegs- oder Krisenprävention, als Versicherung, Verhütung kriminellen Verhaltens oder Vorbeugung sozialer Probleme ? Vorsorgen ist längst zum Alltag geworden. Die Autoren des Bandes erkunden dieses moderne Gesellschaftsphänomen und fragen nach seinen Voraussetzungen und Folgen. Sie widmen sich den Anbietern und Empfängern, Anhängern und Gegnern, den Profiteuren und Leidtragenden. Die Studie bietet damit erstmals eine ebenso facettenreiche wie fundierte Gesellschaftsgeschichte der Vorsorge und eröffnet neue Einblicke in den Wandel moderner Gesellschaften. 410 0$aSchriftenreihe der Vierteljahrshefte fu?r Zeitgeschichte ;$vBand 115. 606 $aPreparedness$xSocial aspects 606 $aCrisis management$xSocial aspects 606 $aHuman security$xSocial aspects 608 $aElectronic books. 615 0$aPreparedness$xSocial aspects. 615 0$aCrisis management$xSocial aspects. 615 0$aHuman security$xSocial aspects. 676 $a363.347 686 $aNW 2200$2rvk 702 $aHannig$b Nicolai$f1980- 702 $aThiessen$b Malte 801 0$bMiAaPQ 801 1$bMiAaPQ 801 2$bMiAaPQ 906 $aBOOK 912 $a996440647603316 996 $aVorsorgen in der Moderne$92742750 997 $aUNISA