Fractales y Formas Arquitectonicas

5/13/2018 Fractales y Formas Arquitectonicas

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b|rw `tgatw|b*kbtw |bigzbAbdb mjdgij nb ajkagl dj wkb b|rw tgatw|bd`cg|gktg vg|j q`gmv|g i`hbdbq b ib @dgb dg iblgiigzb dg ib cj|mb kbtw|bi rwg ajkt`gkg ib @dgbdgi j|dgk dgi grw i l| j p dg ib b|mjk`b+ T|ba a j-kbimgktg qg nb d cg|gka bdl ib b|rw`tgatw|baibqàb dg ib lb||jab ib |ba`jkbi dg ib j|rbkàb ?, +b t|bsgq dg ib n`qtj|`b qg vg|vgtwbk djqtgkdgka bq d`qt`ktbq wkb nba b 26|ba`jkbi phgjmgtkgj jt|b nba`b 26 ||ba`jkbi p 26j|rbk`-aj+-: Gk hgkg|bi ijq bwtj|gq ajkq`dg|bk rwgqjij ib b|rw`tggtw|b lb||jab*j|rbk ab i gkg|giba jk abk ib kbtw|bigzb+ Q`k gmlb|hj ibb|rw`tgatw|b aibq ab*|ba jkbi qg |giba`jkb abk 2 6kbtw|bi b t|bsgq dgi vb|bd`hmb dgi j|dgk dg ibblqt|baa jk dg igpgq kbtw|bigq m gkt|bq rwg ibi`kgb j|rb|wab |gqvjkdg bi mjdgig dg ijqv|jagqjq p ibq igpgqdgi abml`j+( G@ t|bkqaw|| |dg gqtjq djq vb|bd`hmbq gk gi t`gmvj kj gqi`kgbi bvb|gagk p dgqbvb|gagk qg mgzaibk pqwvg|vjkgk+ G@ l|gs q mj awbd|j n qtj| ajt|bzbdj b ajkt`kwba`jk kj t`gkg ib `ktqka`jk dgnbgg| wkb a|jkjijh`b+ dg ib |giba`jk b|rw tqatw|b-kbtw|bigzb k` wkb aibq c aba jk q`kj ib dgdgqtbab| bihwkbq gqagkbq dgkt|j dg ib tgj| bp ib v|b~ q kgagqb|`bq vb|b ib aj|kv|gkq`jkAjmj dàg \gkbtj dg Cwqgl , + + gk ib n`qtj|`btjdj gqtb qwogtj b wkb ajkt kwb t|bkqtj|mba`jk?vg|j nbag cbitb |gqjisg|qg b t ob| ibq d sgtqbqg~v|gqjkgq dg ijq mjmgktjq mbqv|grkbktgq,+,3 Higd jk+ Q hc | gd+ Gqvba+ j+ t g|kvj p b|rw(tgatw|bDjqqbt+ Mbd| d 208>8 Ijq djq vb|bd`hmbq b|r+` tgatjkàjq gqtqk dbqb|j-@@bdjq gk Iw`q Cg|kbkdgz Hbi`bkj+ G@ Cwghj p ib Mg-mj| b qjl|g b|rw` tgatw|b p gkg|h b Bi bkzb Mbd| d2002+> Dg Cwqaj \gkbtj Qtj|`b g qt|wttw|b+ @gjkb dgiibqtj| jr|bt b b|an tgttjkiab Kbvji 2086

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G@d`qqkj dg ijq tgmvijq h|ighjq qg lbqblbgktjkagq gk ibq v|jvj|a`jkgq dg ib+t`rw|bnwmbkb G@ njml|g gq ib mgd`db dg tjdbq ibqabqbq p ibq `dgbq dg q`mgt|`b |`tmjb|mj-k`b p v|gvj|gigk gkawgkt|bk qw j|`hgk gk gibkbiq q dgi awg|vj+ Ib lbqg dg ibq v|jvj|a j-kgq b|rw tgatak abq bkt|jvj|kj|c abq cwg ibqgaa`jk bw|gb Q@ l gk ib b|rw tgatw|b kj `|k tbk khwk gigmgktj gqvga c aj g~ qtgktq gk ibkbtw|bigzb nbag |gcg|gka`b d |gatb b ibq v|jvg|-aijkgq dgi awg|vj nwmbkj p b ib |giba jk gkt|gqwq vb|tgq dg ib rwg qw|hg wkb kj||kbt`sbgqtgt aj-ajkqt|wat sb+ Ijq 3|dgkgq qg dgc`kgkajmj ib d qvjqàjk |ghwib| p vg|cgatb dg ibqvb|tgq tjdbq ajkaw||gktgq b ib aj|kvjqà jk dgwk lgiij ajkowktj G@j|dgk kj gq q |kvig|kgktgwk gk|`rwga |k`gktj j|kbmgktbi dgi gd c a j q kjwk ajkt|ji dg ibq v|jvj|a jkgq dgi |k q|kj+ Gqtbq`dgbq twg|jk |gh`qt|bdbq p dgqb||jiibdbq vj| > 2b|rw tgatj |jmbkj s t|ws j+ .>> BA- QtJ gq q`k wk abiawij g~batj dg qwq m`gml|jq ajmj wknjml|g l`gk cj|mbdj ++ Q` bq" ajmjwqj ib kbtw|bigzb biawg|vj nw-mbkj dg mjdj rwg abdb wkj dg qwq m`gml|jq aj||gqvjkdb v|j-vj|a jkbimgktg b ib qwmb tjtbi c hw|bdb vb|gag qg|rwa l`gk gqtblig-a`g|jk ijq bkt hwjq rwg ib jl|b tg|mikbdb p vg|cgatb tgkhb gk awbktjb v|jvj| ajkgq wkb aj||gqvjndgkA@> v|ga`qb dg abab wkj dg ijqm`gml|jq ajk ib ajkagva`3+k hijlbi dg ib jl|b++,

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22 -Abdb vb|tg( dglg+ qg| mgd`db p wk`db b ibq jt|bqvb| mgd j dg i kgbq+ bkhwijq+ t|bzjq owktw|bq p gkibagqp kwkab dgqaxidbdbmgktg Q`kj abk wkb j|dgkba`jkg~batb p l`gk dgtg|m`kbdb+ Igjk Lbwt q tb Bilg` ti + Dg\g Bgdìàbtj|`b Ijq d`gz i`j|jq dg ib b|rw`tgatw|b.24>7) Bebi Mbd|`d 2002

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Gk gi q`hij ^S@@@nbp wkb lwqrwgdb dg cj|-mbq gqgka`bigq gk wk `ktgktj vb| gkajkt|b|ijq sbij|gq -bwtgkt ajq- p -j| r kbigq- dg ib-gdbd dg j|j, gk ib rwg gi njml|g s`s`b gkgqt|ganj ajktbaij ajk gi hgkWikj j|dgk dg ibkbtw|bigzb- Qghwk Cjw|kbp -ib b|rw`tgatw|bdglg |ghgkg|b|qg mgd bktg ib rgj|kgt|cb- Gkijq v|jpgatjq dg ib gvjab nbiibmjq abkt`dbdgqdg cj|mbq hgjmgt| abq vw|jq+ G@ wk sg|qj gqajkagl dj ajmj bihj qwmbmgktg blqt|batjdjkdg ib kbtw|bigzb gqt i zbdb rw g|g vb|gag|mbq kbtw|bi rwg ib kbtw|bigzb m`qmb+ Aibwdg-Kàjibq Igdjw~ .2813-2>63) wt i zb v|jvj|a`jkgqmjdwib|gq p hgjmgt| abq t|bzbdjq c|gawgktgqqqaa`jkgq bw|gbq p gi wqb dg ibq c`hw|bq q`m-vigq? awbd|bdj+ t|iLkhwij a |awij v |bm`dgqawljq a i`kd|jq gqcg|bq gta+, Gqtbq cj|mbqq`mvigq gqtbk ab|hbdbq dg q`mlji qmj? ibgi vqg .@b |jtba 3k dg ijq vibkgtbq) ib v`|bm|dg.ibq i ibmbq) ib gqcg|b .@b T`g||b) ijq a`|awijq .ibqc|wtbq ibq jkdwiba jkgq dg wkb v`gd|b b||jobdbbi bhwb gta+) Ibq vibktbq qjk q |kgt| abq gktjdjq ijq qgkt`djq p ajkcj|mbdbq vj| gqtbqtj|mbq hgjmgt|àbq+

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B c kgq dgi q`hij ^@ \jlg|t S`qgng| dgqb||ji ib ibtgj| b dg ib gmvbt`b 6 G`kcJniwkh+ Gk qwi l|b ,Qjl|g gi qgktm gktj dg ib cj|mb S`qwbi,.2>82+, Ib gmvbtb |gv|gqgktb gi dgqgj nwmbkj dgcb|mbq kbtw|bi`qtbq j|rbkàbq S @ qang| ajkq`dg-|b gi qgkt`m gktj ajmj wkb bat s`dbd gqv | twbirwg bqwmg qwq cj|mbq dgi g~tg| j| ajmjq`mljijq dg qw v|jv`b s`db b abwqb dg ibgmvbtb rwg q`gktg vj| gibq dg ib bkbijhbgkt|g qwq v|bv jq qgkt |k qktjq `kt`mbq p ibqtj||kbq g~tg| j|gq p dg qw `mvwiqj vbktg qtb dgwk`jk ajkgi mwkdj+ Q` l`gk ijq gqtwd`jq qjl|gv|jvj|A`jkgq ajkt kwb|jk ib bkt`hwb t|bd a 3klbqbd b gk gi vb|bigi qmj g~ qtgktg gkt|g gidgqb||jiij dg ibq igpgq |kbtg|kbt abq dg ibkbtw|bigzb p gi dg ib b|rw`tgatw|b abk ibG`kcJniwkh gi gigmgktj |kbtg|kbt aj v`g|dg qwsbij| dg q`mljij blqt|batj vb|b bqwm`| wkq`hk c abdj dg | tmj j|rbk aj dg gigmgktj dg|giba`jk gkt|g b|rw`tgatw|b g `kd s`dwj+

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Vb|b gi |ba`jkbi q|kj ib hgjmgt|`b gq ib d qa vi -kb rwg j|rb|wzb p j|dgkb ib b|rw`tgatw|b`ktgkgiba jkbkdj ibq d sg|qbq vb|tgq dg ibga t aba jk vb|b ijh|b| gqb b|mjk b gkt|g gitjdj p ibq vb|tgq dg ib rwg nbliblbk ijqt|btbd`qtbq aibqàjq Awljq ajkjq gqtg|bq+akkj|jq p v`|b|k dgq qjk h|bkdgq cj|mbqv|m b|`bq Gqtbq cj|mbq qjk ibq cj|mbq mbqlgiibq pb rwg qjk tbaìgq dg igg| i @Ig Aj|lwq g| wqb t|bzbdjq |grwibdj|gq+ Gk iblbqg dg gqtg ajkt|ji gqtb ib ajksàa`jk dg rwggk ib b|rw tgatw|b qjij vwgdgk hb|bkt zb|qg|giba jkgq b|mjkjqbq awbkdj ijdjq ijqgigmgktjq dg wk gd c a j qg bowqtbk b a`g|tbq|giba`jkgq kw|kg| abq rwg hwb|dbk wkb s`kawib-a`jk ajkqtbktg ajk tjdbq ibq agmbq dgi gd`cà`jB@ `hwbi rwg ibq igpgq aibq abq dgib v|jvj|a 3kgi isijdwij|, dg Ig Aj|lwq`g| gq ib mbt|`z dg ibcj|mb 6 gqt|watw|b a|gbt sb rwg v|gtgkdg qg| wk`kqt|wmgktbi dg bvi aba 3k hgkg|bi gk ib b|rw -tgatw|b p wkb tgakàb vb|b ajk qw bpwdbajkqghwi| wkb mgd`db b||kjk ab gk gi v|jpga-tj Ib cj|mb rwg kbag gqtb s`kawibdb b wkbmbt| z rwg vg|mbkgag `ks`q lig dbdj rwgwk abmg| tg gq wt i zbdb ajmj ng||b|k`gktbbw~ì`b| p ajmj mgd`j rwg ajkt`gkg `dgbq Ib|kbt|`z dg v|jdwaa`jk |gqvjkdg b ib sjiwktbd dg -5njmjhgkg`dbd Q k gmlb|hj tjdbq gqtgqv|ka v jq t gkgk ib lbqg gk wk v|jcwkdj gqtwdjdg ib hgjmgt|`b dg 2+>kbtw|bigzb dg ib awbi qgg~t|bgk |ba`jkbi|kgktg igpgq hgkg|bigq ,Ib hgjmgt| b ijq gOgq ijq a`|awijq p ijq bkhwijq|gatjq i+jdbq g qtbq ajqbq qk sg|dbdgq dg 21hgjmg | b + ++ Ib hgjmgt| b gq gi igkhwbo> dgi nj|kl|g+Ig Aj|lwq`g|20 Mjdwij|(= m3dwij%qgaa`3k dg j|j Q`qtgmb dg|kgd+dbq `dgbdj vb| Ib Aj|lwq g| lbqbdj gk g| awg|vjnwmbkj p ib qgaa`jk bw|gb2gqv`| tw dgi b|lji ib b|mjk`b dgwkb ajkanìi b ib cj|mba`3k dg ibq kwlgq gi owgrj tbii|àj dg ibq jibq rwg qb g~t`gkagk qbl|g ib b|gkb pdgqawl| | ibq g~v|gq|jkgq qwagq`sbqdg wkb cwg|zb`ktg|kb vb|b rwg ib mbkb .ajk ib ablgzb vj| dgt|bq) qgbvbq`jkg vb| gqtb lwqrggjb `kt`mb, Ig Ab|lwq|g| 2013b ijq b|rw tgatjq qwdbc | abkjq

1*70 qqtwd`bkdj ibcj|mb dg ibq kwlgq dw|bktg mgqgq p nbqtb v|gvb|jbvwktgq vb|b wkb -qmtb~`q dg ib mj|cjijh`b dg ibq

kwlgq+ Ajmj sgmjq gqtj jaw||ij bktgq dg rwg gkijq bkjq (86 gi mbtg mbtàj Lgkj`t Mbkdgil|jtdgtg|m`kb|b rwg ib hgjmgt|`b c|batbi gq ib hgjmgt|`bdg ibq cj|mbq kbtw|bigq p gi @kqt|wmgktj bv|jv`bdjvb|b ib dgqa|`va`jk dg ajqtbq kwlgq p |kjktbkbq+

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L`li jtgab dg Tbmvg|g \g mb V gt ib h|bc`gD c|batb i p gqabig|b


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qtgsgk njii

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Ijq a|`tg|`jq dg cj|mbi`zba`3k dg ib mbiib dg ijqab||wkjq p ibq vibzbq ajmj tjdb ib |gd dg `kc|bgq-t|watw|b dgi ob| dk >2kgrj ijq d|gkbogq gtaq`hwgk gi m`qmj a| tg| j dg tj|mba`jkbwtjqgmgobktg g `tg|bt`sb dg ijq c|batbigq Ab| ijqCg||btg| g~viàb rwg ,nbl|b vb|t`dj dg wkb `dgbb|l`t|b|`b gk ib ajktj||kbaijk dg gqtb mbiib p babljbvb|ga`gkdj wk j|aqk+,1< Cg||btg|Ab|ijq Wkb s`qij| vb|tàwib| Kjtbq dgqdggi Qw| 4 Aj|djlb 2007

Mbi b t|`bkhwib| gk > 2 Vb|rwg Ljtbkàj dg Lb|agijkb Ab|ijq Cg||btg|Ojqgv Iiw q Abkjqb Lgt C`hwg|bq


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vgtg| g`qgkmbk

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gogmvij ibgqabib nw|kbkb)+ Gk ib mgtbtj|b dgG`qgkmbk gk abml`j gi |gqwitbdj kj t`gkg sbij|gqtgtàj pb rwg ibq `|kbrgkgq qg wkgk q`k k`khwksbij| b v|ij| i . a g|tjq o wa jq ajmj vb|gag q twbdj- 6,qg bqj|kgob b wk bktgagdgktg n`qtj|àj-+ kj t`gkgkk`khwkb |giba`3k 6 `|kvj|tbka`b)+

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ikqa| va jk .dgob| wkb mb|ab 6 nwgiib) p qwvg|vjq jtjkqjk tbatàbq dgi qabi kh Ib `kqa | va`jk dg ibq mb|abqdg ibq d q t ktbq gqabibq vg|m`tgk `| |gsgibkdj qwagq sb-mgktg d`cg|gktgq |gb i dbdgq Ib |gqwitbktg kj vwgdg qg|v|gd anb q`mvigmgktg dg ib `kqa | va`jk dg B qjl|g L +Gq qjij h|ba bq b wkb vb|t awib| `kqa| `va `jk -dga`mjq 2bqwvg|vjqà`jk dg B qjl|g >- rwg gi |gqwitbdj gq A+Awbkdj B gqtb `kqa| v tb qjl|g L qg mtgktb gkajkt|b| ib@kajhk tb gqajkd`db 6 |gv|`m`db gk A p kj gk gi q`mviggsgktj dg B qbl|g L G@ qab i kh c|batbi v|jdwagc`kbimgktg ib `dgb dg ibd`qajkt`kw`dbd jvwgqtb bijq `dgbigq dg ib b|rw tgatw|b aibqàbGkgqtb b|rw tgatw|b gktgkd db ajmj wk vbi`mvqgqtj qg`kt|jdwagk nwgiibq dgi v|jagqj+ Brw` 2bb|rw tgatw|b kjaig||b k` wk t ab q kj rwg bl|g p diqvg|qb c|bhmgktb pdgqgqtbl i zb gq+wkb g~vij|ba jk dg qw |giba 3k ajk ibqmwtbktgq ajkagva`jkgq dg ib kbtw|bigzb p gi vgkqbm`gk-tj dgi njml|g

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dbk`gi+ i`lgqe`kd

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Wk b|lji qghiik Gwai`dgq

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Ijq @-qpqtgmq qjk q`qtgmbq a|gbdjq b vb|t | dg ib`dgb dg B| qtid i+pkdgk|kbpg| dg ,bwtjmbtgqagiwib|gq, ajmj mjdgi bq dgi a|ga`m`gktj dg ijqqg|gq S@SJQgk 203>+ G@gqtblb @ktg|gqbdj gk ijqdgqb||jiijq dg ibq agiwibq p gkgi a|ga`m`gktj dgibq |bm bq dg ijq b|ljigq+ Wk bwtjmbtb agiwib|gq wk wk sg|qj b|t c` a bi abk q`mvigq igpgqkbtw|bigq+ >g gi rg ibgqt|watw|b dgi wk sg|qj pibq igpgq rwg dglg jlgdgag| p qg dgob rwg gqtgq`hb ibq igpgq vj| qw v|jv b awgktb+ V|bh|bmbk-dj gqtbq igpgq gk ib gjmvwtbdj|b qg vwgdgq`mwib| ib gsjiwa jk dgi wk`sg|qg+ Qg dgkjm`kbk,jqiwib|gq, vj|rwg ajkq qtgk gk agiwibq rwg Q gd`s`dgk p |kwit`vi abk ajmj agiwibq |gbigq+ Vb|ba|gb| gqtjq r|bc ajq qg q`rwg gqtg v|aagd |k`gk-tj+ Qg gjm`gkzb vb| wk t|jkaj rwg qg d`s`dg gkdjqd |gaa jkgq 6 |bmbq p qg |gv tg gi v|jagd -m`gktj gk +gig~t|gmb c`kbi dg abdb |bmb+ G@|gqwitbdj gq wk b|lji w jt|jq jloqtjq qj|v|gk-dgktgq ajmj vjdgmjq jlqg|sb|+

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Ib qgigaa`jk dg ibq c.)|mbq gq ib v|`mg|bdg ibq gqc|btgrobq+vb|b ib t|bdwaa jk K khwkbcj|mb k` ibqaibqàbq k` ibq mjdg|kbq k` ibqc|batbigq qjk hb|bkt`bq dg lgiigzb G@ j|dgk gqqjibmgktg wkj dg ijq cbatj|gq rwg dgtg|m`kbkrwg ib cj|mb tgkhb wk ajktgk`dj gqtgtàj Pbwkbq" kj tjdjq ijq c|batbigq qjk lgiijq |wtjdjqqjk g~v|gq`sjq+ Jt|jq kj i`gkgk rwg sg| ajk giiwhb| 6 abk ibq cwka`jkgq p wqjq rwg |grw`g|g ibjl|b b ajk gi j|dgk ajktgk`dj gk ibq |kbtg|`bqrwg 26ajkqt|w`|bk b abk ibq `dgbq rwgdgqgbt|bkqm`t`| gi d qg|`bdj|+ Dglgmjq ajkc`b| gkkwgqt|jq a| tg| jq ajmj b|rw tgatjq vb|b gigh | p

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|ga|gb| gqtbq cj|mbq+ Dglgmjq dgqb||jiib| kwgqt|babvbadbd vb|b gktgkdg| ibq |giba jkgq gkt|g ibcj|mb ibq @dgbq ajktgk dbq gk ib |k qmb p ibq rwgdgqgbmjq g~v|gqb|+

Ib |ggiblA)|ba`jk dgi gqrwgmb dg j| hgkgq jt|b gqt|btgr b+ Qg qbigaa jkbk gigmgktA`q qg|ga|gbk qwt igq bvjqa jkgq qg v|jvjkgk igatw-|bq+ Ibhgjmgt|b dgob dg qg| jqtgkqsb d`|gatbvbqb b qg| gigmgktj qwlpbagktgdg j|dgk pajkt|ji mbtg|`b vb|b gi v|jagqj dgb|rw`tgatw|`zba`jk+ Bq` ajmj IJW@QEbnk t|blbob-lb abk gi awlb vg|j kj ajkqt|w`b awljq dglg-mbq gktgkdg| rwg ib cj|mb c|batbi rwg qg wtì`zbgq wk gigmgktj dg ajkt|ji dgi d`qg|`j p kj gidiqgkj m`qmj+

Dgkt|j dgi gqrwgmb j|dgkbdj| c|batbi dglgmjqgigr`| awbigq qjk ijq gigmgktjq djm`kbktgq p +awbigq qjk ijq qwlj|dkbdjq gq dgx t|blbob|ibq og|b|rw`bq+ Ib gqt|watw|b c|batbi l| kdb wkvibkj dg wkb a`g|tb wk`tj|m`jbd gk ib rwg dgqtb-abmjq bihwkjq gigmgktjq qbl|g jt|jq+ Vj||bzjkgq q`ml32àbq cwka`bkbigq b gqt|watw|bigqvb|tgq dgi gd c a`j tgkd|bk mbq `|kvj|tbka`b rwgjt|bq+ Qg qwl|bpbk gktjkagq a`g|tbq vb|tgq vb|b`kq`qt`| gk gi qgkt`dj dg ibq @dgbq qg a|gbkagkt|jq dg bt|baa`jk p qg hw`b ib btgka`jk dgijlqg|sbdj|+ Dgkt|j dgi gqrwgmb gqtj qg ijh|bmgdbktg gi wqb dg tb|kbkjq g~agva`jkbigq wkbcj|mb wk ab 6 wk g|kvibzb|k`gktj gqt|btgràj

B vb|t`| dgi gqrwgmb b|dgkbdj| qg |grw`g|gwt i zb| ib gqt|btgr b dg ib awbiitiabgtgk+ Bq"ajmj qg nbag wkb qgigaa`3k dg gigmgktjqv| ka vbigq p qgawkdb| jq abdb vb|tg dglg gqtb|gqtwdbdb gk awbktj b qw ajkj|ga jk+ Ibq awbi -

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Fractales y Formas Arquitectonicas

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