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Titoolroi ginLaleoes b f;reatcsta ls © 19751.984e1 987B enoBi.tM andelbrot ©1 987G iulEiion aueddii tos.rp e. Tao rino .• ISB8N 8-06-59626-8 BenoBÌ.tM andelbrot BIoIg g81111pallall Formcaa,s eod imensione Ediziiotnael iaca unrada iR oberPtiog noni Indice p.I X Prefiaozanlle' eidoiinztea ldiiLa uncPaae leiA tnig eVluol piani XVII Notaa lli'zeidiotnaeld iiRa onbae rPtiog noni Gloig geftrtait tali 3 Prfaezidoenlleu' taoarlesla e coenddai zfriaonncee se 7 I. Introduzione 9 DovJee aPne rrin deevgoolgciga e ftatmii ldiifa orrimi ar rego- laroi en toetrtra I I Intoar ndou e dgior raddiinn eecl oa sl:o' rdienuec lield e'roo- dinfer altet a 12 Conceptrtoip ocsotmsieo luzdiiomneen:s eifofneet ftiigvuar,a ed imensfiroanlteit a 17 Quesstaog gmieos codleal iberadtiavmuelngtaeez l iaovnoer o dir icerca II.Q uantèol ugnal ac osdteal Blrae gtnaa? 2I Differemnettio ddimi i sura 23 Id ateim pirdiiLc eiw iFsr Ryi chardson 24 Primfeo rmdee ldliam ensfiroanlteet a 25 Dimens(ifornaet dtica olnet)e noud tiom,e nsdii Hoanues dorff- Besicovitch 26 Duen oziionntiu ietsisveen: zo imaoltieitnitae erc naas cata 27 Modelsloom madreilocl oas dtiua n i'so:ll acau ravf ai ocdcio nevdeiH elge von Koch 29 Ilc oncedtidt iom ensdiioo mnoet eDt.Ci uar vfer atctoaDnl i comprtersIaa e 2 3I Ilp robldeempiau ndtoip .pL iac urdviaP eancoh rei emipli e piano 32 Senfsios dieclodl iem ensfiroant,iqt uaalnicdiov siieit plaa s- saggaillo i m.iT taeglailopl iec ceoa llegl rea nsdcia le VI INDICE IIII.lr uodloec la so p.4 5 Utilizzadzeilo npecera m siog lioilm roadreeld ilc oo sctoas titui tod alcluar dviaK och 46 Casos empliceimnevnotceeac taosp oi enamdeensticetr to 47 Tracdceimlao tbor owniPaenrocn.h oécn o stituunmi osdceel lo accettpaeburin lcae o sta 48 Lan oziodinc eo nfigurcaazsliuepoa rniem aria IV.R affidcihe er rori 52 Lat raissmsidoendiea ti 54 Modello apprdoirs asfifmdiaicet hrierv olorpa io :l vdeiCr aen toirn,s ifermaelt edt ida imenscioomnper tersOaae I 55 Numermoe didoie rrnoermlio delclaon toriano 56 PoldviCe anrteo trr oncera atnad ozmaitzcao,n dizmieonntaei stiaoznaria 59 PolvdeirL eé vyo,tt enuatp aa rtdiarlerl eat rteas ecadnedio « tre»mi anm odcoa suale 67 v. Ic ratdeerliLl uan a 74 VI.L ad istribudzeilgolanele a ssie 75 Lad ensgiltoàb daellegl ael assie 77 Le iedsesee nczhipeao lrit aau nnom odelflroa tdtida ilset ribu ziodneel glael assie 79 Lu'nivegresroa rcshtircedotiF t oou rnier 81 Lu'nivedriCs hoa rldiide irm,e nseifofneet itnidveat erminata inu ni ntervallo 82 Ipla raddoesclsi oe ilnof uaotcod,e tdtiOo l bers 83 GiustifidciDa zIi doapn aer dtiFe o urnier = 83 CascdaitH ao ylGei.u stifidciD3 2Ii cooninecl r itdeisr tiao- = bildiiJt eàa ns 85 Princciopsim oloecg oiscmoo grafico ·86 Cosneguedniqz uee sdtiiv eprrsiin cipi 87 Digresssuialorlng'eo mednetsioi d ta'ir redsetvloo ldoiR ay leiegs hu ldliam ensDi o2n e = 90 Unc oncegtetnoe raldiidz ezniastteào , u ons's ervaszu'ileolne spansdieo'lunlnei verso 90 L'uinverdsios semiunnna utoovm:oo deldlido i stribduezlione leg alassie 91 Sidta'ir redsiut nov oldoiL évLye.g alacsosmipeeo lvferraet tadlied imensDi< o 2n e 92 Confrocnotgnol e ir rotreil efonici 93 Univefrrsaito ttatlie penrum teiz zdoia gglutisnuaczcieosnis ive INDICE VII VIIM.o deldleirl i liteevror estre P·140 Prelimcianmamriian:li e atori sEefnfzeNat otèleo ad ec fcfie.t - toG iuseppe 105 Motbir owniani frazionari 180 Modelblroo wnidaenrloi liteevror eess ttrrueur tdate lcloes te oceaniche II O Modelblroo wnifarnaoz iodnearlri iloi evo 112 Superpfriioceit tdievliels eo le II3 Iplr obldeemlasl uep erdfeilica ig hi II3 Modelflroal tedt ealslpeo nduen b daic ifnlou viale 162 VIILIa.g eometdreilatl uar bolenza 192 Comed isgtuientrreta u rboleel natmoi nnaerlaelt 'mosfera? 130 Lac ascdaiNt oav ikotve-wSart 131 Comportamdeenltdloia m ensfiroanlteent ea'lilntersezione. CotsruzidoiCn anet airnp idui mensioni 133 Insiemi aslspita aztiia sltCliaanc tio r 153 Les ingoldaerleilqteuà a zdiioN navii er·Sstoonkfoer sal tit?a Quesftaot pteor metitnefridànir e i solverle? 137I X.I ntermitrteelnaztai va 138 Definidzeidiou ngeer addiii n termittenza 138 Misufrrata lated iB esicovitch 139 Caosm oltipligceanteirvaol:i zazlaezaitdooenrleiml aia s ura fraltedt iBa esicovitch 142X . Saponeig l,ei s ponecnrtiitc iocmied imensioni 143 Prelimiinnacraes:t odnita rtiuarnag oli 143 Unm odelldoes la ponbea sastulol 'incasatpoollnoanitaduneraia cerchi 164 XI.O rganizzazdiico onmep onednict ail colatore XIIA.l bedrigie rarcohd iica l assifiecl aadz iimoennes,i one 194 Albelresisi cogreal fali ecgig,e fdreelqlueed nezlpela er ole (Zpif.Mandelbrot) 153 Alberdiig erarecd hiisat,r ibduezriie odndseia tlia (rlieaglgie di Pareto) 155 XIILIe. ssidcenoie ogliosmi XIVA.p pendmiactee matica 158 C'bèi sodginuo n dae finimzaitoenmea dteificr atal ati? 159 Dimens(ifornaet dtica olnet)e ond uitmoe nsdiiHo anues dorff Besicovitch VIII INDICE MisudriHa a usdoBrefsfi-covitch Dimens(ifornlaiit d)tir a icompernit o CotnenudtiMo i nkowski Dimens(ifornlaiit d)tic a oncentrpaezurin omani es ura (Man delbrot) Dimenstioopnoel ogica VariaablielaitL oérviye- stabili Vettoarli eaLtéovr-yisb tiali Diverse fburnozwinoinain e XV.S chibzizgior afici 186 LouBiasc he:l1 Ii mearrz1o78 0- 2a8p ri1l49e6 172 EdmunEdd warFdo urndiA'elrb 1e:68 81-933 137 PauLlév y1:5 se ttber1me 886- 5di cem1br9e7 1 167 LewiFsr Ryi chdasroInI:o tto1br8e8- 13s 0et temb1r59e 3 187 GeorKgien gsZliepy7fg :e nna1i09o2- 2s5et temb1r5e9 0 108 XVIC.o dap,o stscrirpitgnurma ziea menti 158 Rfierimentia ficbii bliogr Prefaazl'idleoinzeii otlnaiea na Delglrea ndeqzuzeelc,lh ahe a u ndai men sioènli en eqau,e lchlneae h ad uèes uperficie, quelclhaen eh at rèec or,p oaeld if uodrii quesntoens i hanngor aanldt.er.zez. e ARISTOTELE Dalelp'odciGa al ilaebob iiammpoa crhaietll oi bdreol la nat«uèrsa c riinlt itnomg autae cmaae,t c iia rastottner riia n go,cl eir,ec dha iltreg efoimgeut»rr.ei cnOhermelao ,n do del lan ostra eqsupoetriildeefin iazgngaua er oem iecthsreo no piutlte'ocscteo:zq iuoèaln lfea o rdmiua ns asdis uon?na u vo lad?iu nmao ntaSgbenbae?pn eeGr a lialnectoha efl oir rmie cadseessroo tlit'mop edreolg leaot mreisatda,if atcthoe la sciehnapz rae feevroiltavone drasanic d eor cqaurecela lrea t teripsitui crhiep foesnton,emic ehdceeo mini nosrfeop rozo tersoess seetrrea tptraidtmauea n gae oemtrpiodaia, aunna' licshipe r ivaisllseraege igotleàla a'rroimn.iI fa enomcehnei noenr asnuost ciebdtiiql uie tsrtaaomt etnntooan v aenvdoi ritdtico id titnaacnozmfaee nomsecniiec nit.i fi D'latpraar, nt ee'elvlolu«zpsioonnnete»aa d elmlaet ema tiche n«amossc»tec rvhiaveni oo laqvuaecnlaolr ea tctheer isti dir elgaoreid tia àr mocnhiseae mbranveacanerosai sgeol gi getdtisi t usdicoi ecnoct:oi Rsfiiie meaW neni erisnttrraosdsu confou nzcioonntici hnneuo ean m metdteornioiv nna etses un pun(teoildm atecmoHa etrimniept aer cloamd eiu n«aip aga lameevnot.ld.eac _ u diit sollgoso g uacrodonor reod ries gu st»oe)P eaunnoca u rva copnatsipsnetauru a ti p tcuihnd eti i unq uad.rA abtboicaomdsoau i n paa rdtefeie nocmheneno in " vengtorntaaostt Ciienilfica;m'peerèhì1éiii-e-èa-re'ii"teme'iiiè ��' ' 1m- -sSÌrljillCéo nad(ri.il.inrl-sd�olemam atemt"ia;dan'al trna u �-�� s�o-oidioegrlr;�r-'-�icEeenceonsTdératoTmpòrt''s�onltoè' Relrcaor re'ffiloèITruzÌone-creièo"ìlceÙib'àse'aeranàI;'imsar'òi ��ii:�i��[t1ia�pprlè!iseipc��eaniszeeld�i iee·':;�o- tn�ira1 i�·.-··' x LUCA PELAINTGIE LeVO U LPIANI Nel«lLae ttreurbaaP toase»u ggecrhicesi ccòhe èe n asco stpou eòs sere pturrocvvheaént goa, cceosrnuc faftioac tiente tenziedo inlei gmeennztcariv;e u oulnei ntelslueptetroi ore petrr ovcaicròhe se hi a s otgtlooic cLhaic .o ntradcdhiez ione abbimaemnoz ioenrsaaot togt looic cdheigs lcii enpzeiraltoi mendoa ll'dienslie zciomolan o o:èn s tartiac onocsocmieu ta taclheie na nni reep creinntcii,pa adol pmeedrniBta ee n oBl.t MandelEbq ruoitn.sd uico o inlt rniobcnuo tnos tiasntiteno ��9E�til.l(é phuern eo mnan cài1oY;q��i�nut ()n 'icdehsaepi :o s � s�E.liclaamr aet emastviiclaup'pa�a ei m (in ma,11sileergl'lata p. Ùi�é.J�JIi��2=:.a�mç, �r._�tt!! z e i<;Q,§tmrait»e maatldilecasi c rI- ziodneefi e nomeni fnianroterucara allciai dut nrtaar nattit a zionanea'niì ca�'"'" "" '"'�'o' ''' pq ''''Èeli�r�tcoh le' oppeiirtina f ludeiMn atned elcbirooèt , illi bqrupoir esepnetlraap t roi vmoal atlla e ttore è italiano, belno ntnaenlosl,usa at rutdtauu nrp ao,n derosod it rattato matemaCtoimcfeaan . o talr'ea usttoers«esm oe,s cdoellai be ratamdeinvtegere snieo rsic,ti rldali av ulgeam zoinoonger a fi»a.I fli dneetl e sntooèn i nfdaitmtois tmraca ornev,i ncere. Quesètl ara a gidoenalepl p'a rente idnci uasiro grodmiennet,i ede semvpein gaollnraoi balvtean,g loansoc ciaadtepire pero, i essere riprepsiitti a mradgia.r diiQ sumoeorscldthtioreon i e, corda quaerllgoo mdeenlltneae dziii aolngoiag lhiil peeirani, segumee diels fiimndoei f: as rv ilunpepllae rteta po orceao pocmoe,d iante diuvnesare snis ieabslilipeltrmeàop pir,ri ietà conosdciqi ubeislutino i vferrasnot uamlaetaotc,oo rssiiiom ,i lea ll'undievlelras eons opsetrreica eo nszia ldoanltla'nuon i vercsoom pasdsealgtleoao mectlraisas ica. Gloig gecthpteoi p olano quehsatnoun nonu onmiev:e rso fratNtoamliee.ns n tu m:er niceivnluo tmohe a,n ancoq uistato esistees noznsaot, ar tiic ononsecciai mupptiiidti i spasroati: prattiunft itsomi aca an,c ihnbe i oloignei cao,n oimnli ian, guisMtaincdae.l èba rnodtaa ct eor claperr eo prcioemtuaànl i laf requenzad edlpelalerl eo'a lullesse to atidsetlilceh ep iene deNli laol;dl ias tribduezlgilaoeln aeesa slisleta r utdteuir a polmoInnoi g.n udniqo u ecsatsioi g,np ii ccpoalrdate el l'og getètu on 'immraigdiondteet lal 'oigngteeEtrctococ.o h sei pongodnupoer oblceommciea: r attecroimzdeze asrcer,i vere