Gli oggetti frattali. Forma, caso e dimensione

226 Pages·1997·14.032 MB·Italian

by  Benoît B. Mandelbrot, Roberto Pignoni (editor)

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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
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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