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“Exista probabil doua cuvinte care exprima capacitatea arhitecturii contemporane de imbogatire

a posibilitatilor de reprezentare si modelare a spatiului: fantezie si libertate si acestea sunt

conferite noii geometrii , tipologii si programe de grafica pe calculator”

“In the mind`s eye a fractal is a way of seeing infinity”

Capitolul 1. Introducere

Capitolul 2. Fractali2.1 Definirea Fractalilor

2.2 Conceptul de Fractal

2.3 Tipologia Fractalilor

2.4 Dimensiunea Fractala2.5 Infinitatea ca parte a vietii

Capitolul 3. Geometria Fractala in rhitectura3.1 Definirea geometriei fractale

3.2 Prezenta fractalilor in r!itectura3.3 "o##ie $ouse% Fran& '.'o(d )rig!t

3.4 ntonio *audi % +agrada Familia

3.5 ,etodologia ar!itecturii fractale.)ater Cu#e

Capitolul !. "ustena#ilitate si rhitectura Fractala4.1 -volutia conceptului de sustena#ilitate

4.2 Prototipuri ale designului sustena#il

Capitolul $. %rase Fractale5.1 e/ Delp!i plan

Capitolul &. rhitectura generata pe calculator0.1 lgoritumul in ar!itectura

0.2 r!itectura parametrica si fractali

Capitolul '. Conclu(ii

T!e main intention of m( researc! is to increase t!e &no/ledge and understandingof natures fractal p!enomena and forms and tr( to appl( t!e results for a #etter

compre!ension of !uman and social #e!aviour and to t!e arc!itectural design.

For more than two decades an intricate and contradictory

relationship has existed between architecture and the sciences of complexity. While the nature of this relationship has shifted and

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changed throughout that time a common point of connection hasbeen fractal geometry. Both architects and mathematicians haveeach oered denitions of what might, or might not, constitutefractal architecture. Curiously, there are few similarities betweenarchitects' and mathematicians' denitions of fractal architecture.

 !here are also very few signs of recognition that the other side'sopinion exists at all. "ractising architects have largely ignored theviews of mathematicians concerning the built environment andconversely mathematicians have failed to recognise the #uitelengthy history of architects appropriating and using fractalgeometry in their designs. $ven scholars wor%ing on conceptsderived from both architecture and mathematics seem unaware of the large number of contemporary designs produced in response tofractal geometry or the extensive record of contemporary writings

on the topic. !he present paper begins to address this lacuna. !his paper focuses primarily on architectural appropriations of fractal geometry to brie&y describe more than twenty years of fractal architecture and to identify %ey trends or shifts in thedevelopment, acceptance and reection of this concept. !he aim of this paper is to provide an overview for both architects andmathematicians of the rise and fall of fractal architecture in the latetwentieth century.

 !he present paper has three clear limitations or provisions whichdene its extent and approach. (irstly, it does not #uestion the

validity of any specic claims from either architects ormathematicians even though there is evidence to suggest thatclaims made by both sides are debatable.)*+ econdly, the paper isconcerned only with conscious attempts to use fractal geometry tocreate architecture. - number of prominent examples of historicbuildings which exhibit fractal forms have been proposed by botharchitects and mathematicians. (or the purposes of this paper theseproposed fractal buildings, including various edieval castles,Baro#ue churches, /indu temples and wor%s of (ran% 0loyd Wrightor 0ouis ullivan, are not considered to be a consciously  createdfractal designs even if they display an intuitive grasp of fractalgeometry. (or this reason, the origins of conscious fractalarchitecture cannot have occurred until after fractal geometry wasformalised by Benoit andelbrot in the late *123s even though4eorg Cantor, 4uiseppe "eano, 5avid /ilbert, /elge von 6och,Waclaw ierpins%i, 4aston 7ulia and (elix /ausdor had all studiedaberrant or mathematically monstrous concepts which are clear

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precursors to fractal geometry. - nal provision for this paper isconcerned with the relationship between fractal geometry and thesciences of complexity. While mathematicians and scholars havevalued fractal geometry in its own right, architects have generallyvalued it more for its connection to Chaos !heory and Complexitycience. !his is because contemporary architects, li%e many historicarchitects, have little interest in geometry or mathematics per se,but value geometry for its ability to provide a symbolic, metaphoric,or tropic connection to something else. !hus, for modern architectsfractal geometry provides a connection to nature or the cosmos aswell as a recognition of the global paradigm shift away from theviews of 8ewton and 0aplace. (or this reason, the vast maority of architects mentioned in this paper view fractal geometry as anintegral part of, or sign for, Chaos !heory and Complexity cience.

Arhitectii apeleaza astazi la calculator si la modele matematice din sfera noilor teorii, dezvoltand

si o arhitectura organica care nu imita aspectele din natura prin decorul ei, ci reflecta ciclul

fundamental al vietii.Stiinta, matematica si tehnologia vin in ajutorul arhitectilor pentru aconstrui o noua dimensiune a creatiilor arhitectonice, in accord cu noua viziune asupra lumii

adusa de teoriile moderne din stiinta

Evolutia dinamicii non liniare au dezvoltat modul de gandire al arhitectilor dincolo de formele de

 baza ale geometriei euclidiene ,precum liniile,patratele sau cercurile.a inceputul secolului !!au fost descoperite noi structure matematice, car ein acelasi timp erau vazute si ca exceptii si nu

se incadrau in tiparele lui "e#ton sau Euclid.

Fractal geometr( a #ranc! of mat!ematics developed in 1s 6,andel#rot 15174 -dgar 138 studies a#stract configurations c!aracterised #( self%similarit(

patterns and recursive gro/t! 6,andel#rot 1748. Fractal o#9ects s!o/ t!eproperties of #eing e:actl( or nearl( t!e same at ever( progressive scale. From t!e

mat!ematical point of vie/ fractal o#9ects are sets t!at !ave fractional dimension

so t!at t!e( are intermediate o#9ects #et/een one and t/o dimensional s!apes ;as

lines and surfaces< or t/o and t!ree dimensional forms ;as surfaces andsolids< 6=att( 175 Falconer 238. "ecentl( t!an&s to t!e development of 

advanced computers t!e domain of fractal geometr( applications !as covered a

/ide set of scientific discipline ranging from mat!ematics 6=er&o/itz 178 naturalsciences pure and applied sciences #iolog( and to engineering and arc!itecture.

Fractal geometr( is specificall( used as t!eoretical as /ell as tec!nical tools for t!e

anal(sis interpretation and description of comple: natural and !uman p!enomena/!ere continuous or -uclidean geometr( are failed to descri#e.

For man( centuries a variet( of natures forms /!ic! in man( cases present fractal

geometr( in t!eir structural appearance suc! as trees cells cr(stals etc. !ave#een creativel( used #( arc!itects and engineers in pro9ects li&e s!ells lig!t%/eig!t

structures arcs tents and #ridges. In t!e past several tec!nical /a(s /ere

e:ercised to connect fractal concepts /it! arc!itecture #( t!e met!od #ased on

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p!(sical modelling process. =ut no/ada(s a procedural generative approac! #ased

on a composition of mat!ematical functions can #e practiced #( using t!eadvantages of contemporar( computer tec!nolog( for connecting t!e fractal

concept /it! arc!itecture ;e.g. Federation +>uare +tore( $all in ,el#ourne?

etc.< 6$u(le#rouc& @ $ammer 208.

Architectural renderings commonl$ sho# projections onto three mutuall$ perpendicular planes,

or consist of cross sections at different altitudes capable of being stac%ed and representingdifferent floor plans. Such renderings ma%e it difficult to imagine buildings comprising ramps

and other features #hich disguise the separation bet#een floors, and conse&uentl$ limit the

creative process of the architect. Analogousl$, #e tend to anal$ze natural structures as if naturehad used similar stac%ed renderings, rather than, for instance, a s$stem of pac%ed spheres, #ith

the result that #e fail to perceive the s$stem of organization determining the form of such

structures.'erception is a complex process. (ur senses record) the$ are analogous to audio or video

devices. *e cannot, ho#ever, claim that such devices perceive. 'erception involves more thanmeets the e$e: it involves processing and organization of recorded data. *hen #e name an

object, #e actuall$ name a concept: such #ords as octahedron, collage, tessellation, dome, eachdesignate a #ide variet$ of objects sharing certain characteristics.