Capítulo - Gerardo Robles

Anuncio
 Capítulo: Robles-­‐Reinaldos, G.(2011). La representación de la realidad. El dibujo compuesto. En: Tornero, P., Simó Mulet, T., Segura Cabañero, J., Robles-­‐Reinaldos, G., (2011) “IDIAA. Investigación, documentación, arte actual”. ISBN. 978-­‐84-­‐92798-­‐46-­‐9. Visión Libros . Madrid. Pags. 113-­‐ 145. LA REPRESENTACIÓN DE LA REALIDAD. EL
DIBUJO COMPUESTO
Gerardo D. Robles Reinaldos
Introducción
Orígenes del dibujo a través de la geometría
/D SDODEUD ´GLEXMRµ GHULYD GH XQ YRFDEOR ODWLQR ´GHVLJQDUHµ
TXH VLJQLÀFD GHVLJQDU VHxDODU (O GLEXMR WUDGLFLRQDOPHQWH KD
FRQVLVWLGRHQGHVFULELURPRVWUDULGHDVRFRQFHSWRVUHIHULGRVD
REMHWRVUHDOHVRLGHDOHV$SDUHFHFRPROHQJXDMHGHFRPXQLFDFLyQ
GHVGH QXHVWURV RUtJHQHV FRPR KXPDQRV FRQ HO REMHWLYR GH
UHSUHVHQWDU PRPHQWRV GHFLVLYRV LPSRUWDQWHV R HYROXWLYRV
FRPRPRWLYRVÀJXUDWLYRVRLQFOXVRGHFDUiFWHUQRÀJXUDWLYR8&
(O KRPEUH SUHKLVWyULFR QRV KD GHMDGR QXPHURVDV HYLGHQFLDV
JUiÀFDV VREUH UHSUHVHQWDFLRQHV GH DFFLRQHV DVt FRPR IRUPDV
KXPDQDV\DQLPDOHVLQWHUSUHWDGDVFRPRHUDQFDSDFHV\FRQORV
PHGLRVTXHGLVSRQtDQ3RUWRGRHOORVHGHGXFHTXHODHVFULWXUD
FRPROHQJXDMHHVGHVFULSWLYD\DVRFLDGDDREMHWRVUHDOHV\SRU
WDQWR VH RULJLQD FRPR XQD HYROXFLyQ GHO GLEXMR HQ IRUPD GH
HVFULWXUD
/DLPSRUWDQFLDGHOGLEXMRHVHQHVHQFLDODGLVWDQFLDPiVFRUWD
GHVGHODLPDJLQDFLyQKDVWDODUHDOLGDG'HVGHODDQWLJHGDGKD
##$
HVWDGRVRPHWLGRDOSODQRELGLPHQVLRQDOVLHQGRPRQRFURPiWLFR
R GH HVFDVRV FRORUHV HQ GLIHUHQWHV JUDGDFLRQHV +D VHUYLGR \
VLUYHSDUDH[SUHVDULGHDVGHFXDOTXLHUtQGROHHVWpWLFDDEVWUDFWDR
ÀJXUDWLYD$WUDYpVGHOWLHPSRHOKRPEUHKDLQWHQWDGRWUDGXFLU
OD LPSUHVLyQ TXH SHUFLEtD GH ORV REMHWRV UHSURGXFLpQGRORV HQ
IRUPDV YROXPHQ WDPDxRV HVFDODV« PHGLDQWH WUD]RV \ PiV
WDUGH FRQVLGHUDQGR OD OX] LQFLGHQWH FRPR DVSHFWR GHO UHOLHYH
(O HMHUFLFLR GH GLEXMDU KD HVWDGR UHODFLRQDGR GLUHFWDPHQWH
FRQODUHSUHVHQWDFLyQGHORVREMHWRVYLVLEOHV\HOUHJLVWURGHODV
VHQVDFLRQHVUHFLELGDVSULRULWDULDPHQWHDWUDYpVGHODYLVLyQVREUH
XQVRSRUWHSODQR
$%7&/52.5*%7&3*+'3%&;&*1,%-%&B1,'-.%*1-&2%7&%*.'7&4'&2%&)+-.5*%&;&
HVFXOWXUDFRPRH[WHQVLyQDPEDVVLHPSUHDODWHRUtDLQH[FXVDEOH
GHO GLEXMR DVRFLDGD VLHPSUH D OD JHRPHWUtD /RV JULHJRV
LQFRUSRUDURQGHPRVWUDFLRQHVHQEDVHDUD]RQDPLHQWRVGDQGRXQ
FDUiFWHUFLHQWtÀFR\IRUPDODODJHRPHWUtD(XFOLGHVHQHOVLJOR,,,
D&FRQÀJXUyODJHRPHWUtDHQIRUPDD[LRPiWLFDWUDWDPLHQWRTXH
SHUGXUyFRPRQRUPDGXUDQWHVLJORV/DJHRPHWUtDHXFOLGLDQDVH
VRVWHQtDSRUFLQFRSRVWXODGRVRD[LRPDV:TXHVHKDQPDQWHQLGR
HVWDEOHV KDVWD TXH /REDFKHYVNL HQ HO VLJOR ;,; SXVR HQ GXGD
UHDOHOTXLQWRSRVWXODGR
3HUR VL H[LVWH XQ SXQWR GH SDUWLGD SRU HO FXDO HO GLEXMR
HYROXFLRQD QRWDEOHPHQWH HV FRQ OD DSDULFLyQ GH OD SHUVSHFWLYD
HQ HO 5HQDFLPLHQWR /D SDODEUD ´SHUVSHFWLYDµ VH GHULYD GHO
ODWtQ 8+&,8#0*(, TXH VLJQLÀFD ´PLUDU KDFLD GHODQWHµ 'XUDQWH HO
5HQDFLPLHQWR/HRQDUGRGD9LQFLHQVHxDEDDGLEXMDUVLJXLHQGR
WUHVHWDSDVVXFHVLYDVSULPHURODFRSLDGHGLEXMRVJHQHUDOPHQWH
GH 5DIDHO R 0LJXHO ÉQJHO GHVSXpV VH FRQWLQXDED FRQ FRSLDV
HQ \HVR GH ÀJXUDV FOiVLFDV \ SRU ~OWLPR GHO QDWXUDO DQDWRPtD
\SHUVSHFWLYDGHSHUVRQDVELHQSURSRUFLRQDGRV5HSHWLGDPHQWH
VH FRQVLGHUy TXH OD FLPD \ Pi[LPD SHUIHFFLyQ GHO DUWH GH OD
SLQWXUDHVWDEDHQODDVRFLDFLyQGHOGLEXMRGH0LJXHOÉQJHOFRQ
HOFRORULGRGH7L]LDQRVHJ~QDSXQWDHQWUHRWUDVUHIHUHQFLDVHQ
<9:)&A&$29$I9**(+:3DROR3LQRWHyULFRGHDUWHYHQHFLDQR
$SULQFLSLRVGHOVLJOR;9,,H[LVWHXQDFULVLVH[LVWHQFLDOLVWDGHO
LQGLYLGXR SRU HOOR HO SHQVDPLHQWR ÀORVyÀFR GH 'HVFDUWHV VH
!!"
IXQGDPHQWyHQXQPpWRGRTXHFRQVLVWtDHQWRPDUXQSXQWRGH
SDUWLGDLQGXGDEOHVREUHHOTXHFRQVWUXLUWRGRHOFRQRFLPLHQWR(Q
VXREUD<9,0(+,&$2#)$K@*&2&SXEOLFDGDHQ/HLGHQ+RODQGDHQ
'HVFDUWHVGLYLGHHQVHLVSDUWHVVXVUD]RQDPLHQWRVTXHGHVWLHUUDQ
ODVYLHMDVLGHDVPHGLHYDOHV\DEUHODVSXHUWDVDODQXHYDFLHQFLDHQ
JHQHUDO\DOSHQVDPLHQWRPRGHUQR'HVFDUWHVIXHHOFUHDGRUGH
ODJHRPHWUtDDQDOtWLFDHQXQFLDGRHQHODSpQGLFHGHO<9,0(+,&$2#)$
C@*&2&HVWDEOHFLyHOVLVWHPDGHFRRUGHQDGDVRUWRJRQDOHVFRQRFLGR
HQODDFWXDOLGDGFRPRVLVWHPDFDUWHVLDQRHQHOTXHVHSUHFLVDQ
GHWUHVUHIHUHQFLDVSDUDORFDOL]DUXQSXQWRHQHOHVSDFLR[\]
(QODJHRPHWUtDDQDOtWLFDVHDUWLFXODQORVVLVWHPDVGHUHIHUHQFLD
FDUWHVLDQRV ELGLPHQVLRQDOHV \ WULGLPHQVLRQDOHV EDVDGR HQ HO
)*+-/+)+1&4'&5-&7+7.',%&4'&/11*4'-%4%7&B1*,%41&)1*&417&*'/.%7&
TXH VH FRUWDQ HQ XQ SXQWR GHQRPLQDGR RULJHQ 6LQ HPEDUJR
QR HV KDVWD HO VLJOR ;,; FXDQGR HO PDWHPiWLFR UXVR 1LNROiL
,YiQRYLFK/REDFKHYVNLGHVFXEUHXQVLVWHPDGHJHRPHWUtDQR
HXFOLGHDQDUHFKD]DQGRHOTXLQWRSRVWXODGRGH(XFOLGHV
+DVWD DKRUD GLEXMR \ JHRPHWUtD KDEtDQ HVWDGR VLHPSUH
UHODFLRQDGRV HO SULPHUR FRPR OHQJXDMH \ HO VHJXQGR FRPR
VLVWHPDDODKRUDGHUHSUHVHQWDUHLQWHUSUHWDUFRUUHFWDPHQWHOD
UHDOLGDG (Q FDPELR \D HQ HO VLJOR ;; HQ HO SRVWFXELVPR HO
GLEXMRQRRIUHFHODUHODFLyQIRUPDLPDJHQFOiVLFDVLQRODIRUPD
UHDOLGDG2ORTXHVHULDORPLVPRTXHHOGLEXMRFRQWHPSRUiQHR
QRWUDWDHQEXHQDPHGLGDGHLPLWDUODIRUPDGHODVFRVDVVLQR
FUHDU IRUPDV RULJLQDOHV QR LPLWDU OD UHDOLGDG VLQR HQFRQWUDU
SDUDOHOLVPRV R HTXLYDOHQFLDV GH OD UHDOLGDG (V GHFLU QR
LPLWDU OD QDWXUDOH]D FRPR XQ SURFHVR PLPpWLFR VLQR DOWHUDUOD
FUHDWLYDPHQWH 8Q HMHPSOR VH GHÀQH FRQ OD VXEMHWLYLGDG GH OD
YLGD HQ ORV 3DLVDMHV LQWHULRUHV GH 3DXO .OHH DQWHFHVRU GHO GLEXMR
DEVWUDFWR
(OGLEXMRJHRPpWULFROOHJDDVXDSRJHRFRQHO´RSDUWµHQORV
TXH VH WLHQH HQ FXHQWD HO HVSHFWDGRU FRPR FRQVWUXFWRU GH OD
LPDJHQ0LHQWUDV0RQGULDQUHFRJHHQVXVGLEXMRVUHFWDQJXODUHV
HO RUGHQ VXE\DFHQWH HQ OD QDWXUDOH]D 9DVVDUHO\ FRQVLJXH
LPSUHVLRQHV YLVXDOHV QXHYDV FRQ OD UHSHWLFLyQ GH PyGXORV HQ
VXV GLEXMRV (O GLEXMR FRQVWUXFWLYLVWD SURFHGH DVLPLVPR D OD
##$
SHFXOLDURUGHQDFLyQGHOtQHDV\SODQRV(OGLEXMRKDLOXVWUDGR
SRUFRQVLJXLHQWHODHYROXFLyQGHODIRUPDTXHKDSDVDGRGHVHU
IRUPDHOHPHQWDODIRUPDFRPSOHMDRFRQVWUXFWLYDSDUDWHUPLQDU
HQHOIHQyPHQRDEVWUDFWR'HVGHORVDxRVVHVHQWDUHVXOWDGLItFLO
HQFDVLOODUDXQDUWLVWDHQXQPHGLR\PXFKRPHQRVD~QHQFRQ
XQVRSRUWHGHWHUPLQDGR&DGDYH]HVPiVIUHFXHQWHHQFRQWUDU
DUWLVWDV TXH GHVDUUROODQ VXV LGHDV HQ GLYHUVRV VRSRUWHV \ TXH
WUDVODGDQ GH XQ VRSRUWH D RWUR FRQFHSWRV HVSHFtÀFRV GH FDGD
XQRGHHOORV
1R VH WUDWD \D GH SUiFWLFDV PXOWLGLVFLSOLQDUHV VLQR GH OD
.*%-7+/+0-& 4'& 217& %*.+7.%7& 4'& 5-& ,'4+1& %& 1.*1& +-/2571& '-&
HO LQWHULRU GH XQ PLVPR SUR\HFWR KDVWD HO SXQWR GH TXH
)5'4'& *'752.%*& )%*%40F+/1& 7'35+*& 4'-1,+-%-41& %*.+7.%&
YLVXDODDOJXLHQFX\DREUDQRHVYLVLEOHVLQRWDOYH]OHJLEOH
RDXGLEOHREDLODUtQDDOJXLHQTXHQRVHPXHYHRLQFOXVR
HVWiDXVHQWHGHHVFHQD/RWUDQVGLVFLSOLQDUSXHGHDIHFWDUD
WHUULWRULRVDSDUHQWHPHQWHWDQDOHMDGRVFRPRODSRHVtD\OD
FLHQFLD<
(OGLEXMRWUDGLFLRQDOPHQWHVHKDFRQVLGHUDGRFRPRHOUHVXOWDGR
GH XQD DFFLyQ GHVFULWD HQ XQ VRSRUWH PiV ELHQ SODQR 3HUR VL
HOUHVXOWDGRIXHUDHQVtODDFFLyQSURSLDGHGLEXMDUHODQiOLVLV
TXH UHDOL]DUHPRV HQ DGHODQWH VH VLW~D HQ WRUQR DO WpUPLQR
LQWHUYHQFLyQJUiÀFDHVWDSUiFWLFDVHHQWHQGHUiFRPRODDFFLyQ
TXHSXHGHHMHUFHUHOHVSHFWDGRU\RDUWLVWDHQODREUDDSDUWLUGHOD
PRGLÀFDFLyQGHpVWDRGHDOJXQRGHVXVFRPSRQHQWHV(OJUDGR
GHSDUWLFLSDFLyQHQODREUD\VXRSHUDWLYLGDGFRQODPLVPDVHUtD
PD\RUSRUVXUHODFLyQPDQLSXODGRUDH[SHULPHQWDO\GLQiPLFD
El dibujo como medio grafico tradicional y su
relación con los nuevos medios
(O GLEXMR KD YHQLGR FRQVLGHUiQGRVH XVXDOPHQWH FRPR
LQVWUXPHQWR GH SHUIHFFLRQDPLHQWR GHO WUDEDMR GH SLQWRUHV
\ HVFXOWRUHV $O GLEXMDU SULPHUR VH OHHQ ODV IRUPDV \ OXHJR
!!"
VH GHVFULEHQ (VWH HMHUFLFLR H[SUHVLYR TXH SXHGH OOHJDU D
GRPLQDUVH WUDV XQ SHUtRGR GH DSUHQGL]DMH \ SUiFWLFD HGXFD OD
LQWHOLJHQFLDKDVWDHOSXQWRGHTXHHODUWLVWDTXHKDGLVFLSOLQDGR
VXSHUVRQDOLGDGGLEXMDQGRDIURQWDFRQHVDPLVPDGLVFLSOLQD\
RUGHQDFWLYLGDGHVHQDSDULHQFLDWDQGLVWDQWHVFRPRODH[SUHVLyQ
DEVWUDFWD
&RQHOLQLFLRGHOSHQVDPLHQWRFLHQWtÀFRHOGLEXMRVHOLEHUD\D
QRHVSDUWHGHODWRWDOLGDGGHXQSURFHVRPiVFRPSOHMRVLQRTXH
DGTXLHUHVXSURSLRHVWDWXVLQGHSHQGLHQWH(OGLEXMRVHFRQVLGHUD
GH IRUPD DOWHUQDWLYD GH DFXHUGR D OD FLUFXQVWDQFLD HQ VX
FRQGLFLyQGHPHGLRJUiÀFRFRPRSRUHMHPSORHQODDUTXLWHFWXUD
R LQFOXVR FRPR REUD DUWtVWLFD *HQHUDOL]DQGR \ VDOYDQGR ODV
JUDQGHVGLIHUHQFLDVGHUHSUHVHQWDFLyQHQWUHHO5HQDFLPLHQWRHO
0DQLHULVPR\HO%DUURFRVHLPSRQtDQODVUHJODVGHOHVSDFLROD
SURIXQGLGDGODOX]HQGHÀQLWLYDGHODSHUVSHFWLYD\GHODUD]yQ
GHODJHRPHWUtDHXFOLGLDQD3HURHOGLEXMRFDGDYH]VHVHSDUDPiV
GHOREMHWRUHSUHVHQWDGRFRPRPRGHOR\ODSURSLDUHSUHVHQWDFLyQ
FRQVWLWX\HXQDREUDHQVt6HHVWDEOHFHODVXSUHPDFtDGHOGLEXMR
FRQXQDYLVLyQDQDOtWLFDGHODFRQVWUXFFLyQTXHSHUPLWHSURJUHVDU
HQODWpFQLFD\FRQODHVWUXFWXUDWRWDOL]DGRUDGHODSHUVSHFWLYD
/D *HRPHWUtD 3UR\HFWLYD FRQRFLGD FRPR HO HVWXGLR GH OD
JHRPHWUtD TXH LQFRUSRUD DO SODQR XQD UHFWD GH SXQWRV LGHDOHV
LQÀQLWRVIXHLPSRUWDQWHHQVXXWLOLGDGSDUDHVWXGLDUSUR\HFFLRQHV
(OUHVXOWDGRIXHD~QPiVUHOHYDQWHHQWUHVGLPHQVLRQHV\DTXHVH
XVDURQSUR\HFFLRQHVSDUDUHSUHVHQWDUÀJXUDVWULGLPHQVLRQDOHVHQ
SODQRVHVGHFLUSDUDSODVPDUGLEXMRVUHDOHVHQHOSODQR(OSODQR
RUGLQDULR FRQ HVWD UHFWD GHO LQÀQLWR DxDGLGD VH FRQRFH FRPR
HO SODQR SUR\HFWLYR ([LVWHQ YDULDV PDQHUDV GH UHSUHVHQWDUOR
FRPRODEDQGDGH0|ELXVTXHWLHQHUHODFLyQFRQHOPRYLPLHQWR
HQHOHVSDFLR
'HVGHODGpFDGDGHORVHODYDQFHGHODVWpFQLFDV\ODH[SDQVLyQ
GHOFRPSXWDGRUFRPRKHUUDPLHQWDGHOGLEXMRKDLGRUHOHJDQGR
SRFRDSRFRDOGLEXMRWUDGLFLRQDOVREUHWRGRHQFDPSRVFRPR
HO GLVHxR \ OD DUTXLWHFWXUD (O GLEXMR LQIRUPDWL]DGR DSDUHFH
FRPR SURFHVR LQWHUDFWLYR \ QHXWUR HQ RSRVLFLyQ D OD VtQWHVLV
##$
SHUVRQDO GHO GLEXMR WUDGLFLRQDO RIUHFH GH XQD IRUPD VLQWpWLFD
OLPSLD \ GH DSDULHQFLD LQGXVWULDOL]DGD (VWD RSRVLFLyQ HV PiV
QRWRULD VL DxDGLPRV XQ LPSXOVR GH LPDJLQDFLyQ FLHQWtÀFD (O
SHQVDPLHQWRFLHQWtÀFRPiVHÀFD]WUDWDSRUORFRP~QGHUHOHJDU
OD LPDJHQ D XQ VHJXQGR SODQR GH UHHPSOD]DUOD SRU VLJQRV
VRFLDOHVELHQGHÀQLGRV6HOOHJDHQWRQFHVDXQSHQVDPLHQWRVLQ
LPiJHQHVTXHUHWRPDUtDSDUWHGHODÀORVRItDDQDOtWLFDGHOVLJOR
;;6HKDEODGHSHQVDPLHQWR\QRGHLPDJLQDFLyQ(QHIHFWRVH
GXGDUtDGHHPSOHDUHOWpUPLQRGHLPDJLQDFLyQHQHOFDVRGHHVRV
SHQVDPLHQWRVVLQLPiJHQHVDXQFXDQGRKD\DGHVERUGDPLHQWR
PDUFKDKDFLDDGHODQWHORFXDOVLPSOLÀFDUtDHOSUREOHPDVLQRVH
SUHVHQWDUDXQDGLÀFXOWDGDQiORJDSRUHOODGRFRQWUDULR,PDJLQDU
HVXQDDFWLYLGDGYLVXDOLQWHUQD
Fig. 1. Ejemplo de la banda de Möbius.
(Q FXDQWR D OR TXH FRQRFtDPRV DFHUFD GH OD LPDJLQDFLyQ \
OD FUHDWLYLGDG IXHURQ ODV LQYHVWLJDFLRQHV GHO QHXURÀVLyORJR
\ SVLFyORJR HVWDGRXQLGHQVH 5RJHU 6SHUU\ TXLHQ HVWXGLy
ODV YtDV GHO FHUHEUR SDUD FRQRFHU VXV IXQFLRQHV 5HFLELy HQ
HO 3UHPLR 1REHO GH 0HGLFLQD SRU KDEHU GLIHUHQFLDGR
ODV IXQFLRQHV GH ODV TXH VH HQFDUJD SRU VHSDUDGR R GH IRUPD
GRPLQDQWHFDGDKHPLVIHULR=(OGRFWRU6SHUU\\VXVFROHJDVGHO
,QVWLWXWR &DOLIRUQLDQR GH 7HFQRORJtD HQFRQWUDURQ LQGLFDFLRQHV
FRQFUHWDVGHORTXHHVHOSRWHQFLDOFUHDWLYRTXpLQWHUYLHQHHQVX
IXQFLRQDPLHQWR\GyQGHVHHQFXHQWUDXELFDGR6DEHPRVGHVGH
UHODWLYDPHQWHSRFRVDxRVTXHHOKHPLVIHULRL]TXLHUGRGRPLQD
HO OHQJXDMH OD VROXFLyQ GH SUREOHPDV OyJLFRV \ HO SHQVDPLHQWR
DQDOtWLFR PLHQWUDV TXH HQ HO GHUHFKR GHVWDFDQ RWURV DVSHFWRV
!!"
FRPR OD FRPSUHQVLyQ HVSDFLDO PXVLFDO R HO GLEXMR $XQTXH HO
KHPLVIHULR L]TXLHUGR WLHQH HO OHQJXDMH HV EDVWDQWH PDOR SDUD
HOGLEXMR(OKHPLVIHULRGHUHFKRTXHGLULJHODPDQRL]TXLHUGD
SRGUtD GLEXMDU EDVWDQWH ELHQ 6LQ HPEDUJR FXDQGR YLYLPRV HO
SURFHVR FUHDWLYR ORV KHPLVIHULRV FHUHEUDOHV VH HQFXHQWUDQ HQ
DFWLYLGDGDOPLVPRWLHPSRIXQFLRQDQGRGHIRUPDFRKHUHQWHH
LQWHJUDGDHQHODFWRFUHDGRUHVGHFLU
$XQTXHFDGDKHPLVIHULRHVGRPLQDQWHHQFLHUWDVDFWLYLGDGHV
ORVGRVHVWiQEiVLFDPHQWHFDSDFLWDGRVHQWRGDVODViUHDV\
GHKHFKRODVKDELOLGDGHVPHQWDOHVLGHQWLÀFDGDVSRU5RJHU
6SHUU\VHKDOODQGLVWULEXLGDVSRUWRGDODFRUWH]D
3HUFLELU VHUtD GLVWLQJXLU VHQVRULDOPHQWH DOJR FRPR XQD ÀJXUD
RSURSLHGDGH[WHUQDPiVRPHQRVGLIHUHQFLDGD6LODGLVWDQFLD
GHOREMHWRSHUFLELGRLQWHUYLHQHHQODSHUFHSFLyQHVMXVWDPHQWH
SRU HIHFWR GH XQ VREUHQWHQGLGR GHO FHQWUR SHUFHSWLYR 7RGR
VXFHGH FRPR VL HO YDORU GHO REMHWR SHUFLELGR DXPHQWDUD R
GLVPLQX\HUDHQIXQFLyQGHODGLVWDQFLDDOQLYHOGHOSHQVDPLHQWR
UHSUHVHQWDWLYR(VWDQDWXUDOH]DGHODGLVWDQFLDHVWDUiGLVLPXODGD
SRUUHSUHVHQWDFLRQHV>
&RQ HO GHVFXEULPLHQWR YLVXDO VH KDFH HYLGHQWH DTXHOOD PDQHUD
GHSURFHGHUGHQXHVWUDSHUFHSFLyQYLVXDODPRGRGHSUR\HFFLyQ
HQ SURFHVR GH DVRFLDUOH XQ VLJQLÀFDGR 'H OR TXH VH WUDWD HQ
HVWHDUWtFXORHVGHXWLOL]DUHVHPLVPRPHFDQLVPRHQXQVHQWLGR
GLVWLQWRSHURFRPSOHPHQWDULRDOGHVFULWRDQWHULRUPHQWH/RTXH
SURSRQHPRVHVXQPpWRGRSDUD´JXLDUµODSUR\HFFLyQPHGLDQWH
OD XWLOL]DFLyQ GH ´HVTXHPDVµ R ´SDWURQHVµ DFFLGHQWDOHV R QR
HQ HO PRPHQWR GH GLEXMDU R HODERUDU LPiJHQHV FRPSOHMDV HQ
XQHVSDFLRP~OWLSOH(OPpWRGRFRPRWDOQRGLÀHUHDSHQDVGHO
TXH XWLOL]DPRV KDELWXDOPHQWH D OD KRUD GH GLEXMDU HQ JHQHUDO
SDUWLPRVGHXQDVHULHGH´HVTXHPDVµR´SDWURQHVÀJXUDWLYRVµ
TXH KHPRV LGR DGTXLULHQGR FRQ OD SUiFWLFD \ TXH YDPRV
JUDGXDOPHQWHPRGLÀFiQGRORKDVWDTXHFRUUHVSRQGDFRQHOWHPD
TXHTXHUHPRVUHSUHVHQWDU
/DLPDJLQDFLyQVHLQFOLQDDFRQYHUWLUVHHQODIDFXOWDGKXPDQDTXH
VHYHHVWLPXODGDSRUORVREMHWRV\HOOHQJXDMHLQGHSHQGLHQWHGH
##$
TXHHVWRVVHRULJLQHQHQHOH[WHULRURLQWHULRUGHQXHVWURFHUHEUR
3RU WDQWR VH UHÀHUH SRU LJXDO D XQD LPSUHVLyQ VXVFLWDGD HQ HO
HVStULWXSRUORVVHQWLGRV\DODLPSUHVLyQTXHHOHVStULWXFRQVHUYD
HQ Vt PLVPR (VWH HV HO VHQWLGR TXH GLFKR FRQFHSWR WRPD HQ
'HVFDUWHV SRU HMHPSOR FXDQGR GLFH TXH OD JHRPHWUtD IDWLJD
ODLPDJLQDFLyQDXQTXHTXL]iVPDVTXHIDWLJDUODODUHOHJDDXQ
VHJXQGRSODQR/DJHRPHWUtDVHFDUDFWHUL]DSRUIRUPDVFHUUDGDV
R SUHYLVLEOHPHQWH FRQFOXVDV $XQTXH SDUD FRQVHJXLU GLFKD
SUHYLVLyQRLQWXLFLyQSHUFHSWLYDVHGHEHUiDSUHQGHUSULPHURD
GLVFULPLQDUHQWUHORTXHVHWLHQHTXHGLEXMDU\ORTXHGHEH\R
SXHGHVLPSOHPHQWHVXJHULU(VWRHVDVtSRUTXHQXHVWURVLVWHPD
SHUFHSWLYR VH HQFDUJD GH VXSOLU ODV OLPLWDFLRQHV GH QXHVWURV
PDWHULDOHVFRPSOHWDQGRPHGLDQWHHOEXHQXVRGHODSUR\HFFLyQ
JXLDGD\GHXQDIRUPDFRKHUHQWHDTXHOORVGDWRVTXHODLPDJHQ
VRODPHQWH VXJLHUH SHUPLWLpQGRQRV GLVFHUQLU GRQGH H[LVWH
FRQIXVLyQ\FRPSOHWDQGRHQXQWRGRJOREDOWRGDHOFRQWHQLGR
GHO RULJLQDO 1XHVWUR FHUHEUR VLPSOLÀFD ORV GDWRV UHODWLYRV
DO WRWDO SUHGRPLQDQGR ODV IRUPDV FRQFUHWDV DVRFLDGDV HQ OD
PHPRULD D VLJQLÀFDGRV 3RU HOOR HQ GHWHUPLQDGDV VLWXDFLRQHV
FXDQGRHOGRPLQLRJOREDOHVGLIXVRSDUDQXHVWURFHUHEURVHFUHD
XQDUXSWXUDGHOPHFDQLVPRVHQVRULDO/RVQLYHOHVGHSURFHVDGR
FDPELDQSRUHMHPSORHQREUDVQRÀJXUDWLYDVRDEVWUDFWDVVXHOHQ
SUHYDOHFHUODVGLIHUHQFLDVGHFRORUHOWRQR\FRPSRVLFLyQ
/DLQWXLFLyQSHUFHSWLYDWLHQGHDFRPSOHWDUODV]RQDVGpELOHVGHO
GLEXMRDIDYRUGHDTXHOODVFRQFUHWDVRIXHUWHV(QHVWRVFDVRVOR
TXHVHSURGXFHHQWRQFHVHVXQDLOXVLyQSRUTXHHQODLPDJHQR
GLEXMRH[LVWHQPiVUDVJRVGHORVTXHVHPXHVWUDQFRPRH[SUHVD
*RPEULFKHQVXOLEUR$.+*#$#$9)(,9B1(QHIHFWRHVXQDLQWXLFLyQ
SHUFHSWLYDGH´FRPSOHWDPLHQWRµGHLPDJHQ
$XQTXHODVÀJXUDVHVWpQSLQWDGDVVLQRMRVWLHQHTXHSDUHFHU
TXHPLUDQVLQRUHMDVWLHQHTXHSDUHFHUTXHHVFXFKDQ>@
(VDVVRQFRVDVTXHGLH]FHQWHQDVGHSLQFHODGDVQRSXHGHQ
SLQWDUSHURTXHXQDVSRFDVSLQFHODGDVVHQFLOODVVLHVWiQ
ELHQ GDGDV FDSWDQ (VWR HV OD YHUGDGHUD H[SUHVLyQ GH OR
LQYLVLEOHS?
!!"
6LQ HPEDUJR 5XGROI $UQKHLP YD PiV DOOi GHVDUUROOD OD LGHD
GHODLQWXLFLyQTXHODGHÀQHFRPR´«XQDKDELOLGDGPHQWDO
UHVHUYDGD D OD SHUFHSFLyQ VHQVRULDOµ S #& 4+7.+-.1& 4'2&
LQWHOHFWR´ODLQWXLFLyQSHUFHSWLYDHVODSULQFLSDOIRUPDTXHWLHQH
ODPHQWHGHH[SORUDU\FRPSUHQGHUHOPXQGRµ
(QODHMHFXFLyQGHOWUD]RVHGHWHUPLQDODIXHU]D\GLUHFFLyQGHO
JHVWR H[SUHVDQGR OD LQWHQFLRQDOLGDG GHO GLEXMDQWH KiELO 3HUR
VXKDELOLGDGQRVHWUDWDVRORHQFRQVWUXLUGLULJLHQGRODPLUDGD
GHOHVSHFWDGRUVLQRHQFRPSRQHUGHIRUPDFUHDWLYDGXUDQWHHO
UHFRUULGRYLVXDO$PRGRGHXQDH[SHULHQFLDYLYDHQHOWLHPSR
HQHOTXHVHYLVXDOL]D/DHYLGHQFLDGHPXHVWUDTXHFLHUWDVOtQHDV
GHVFULWDVHQODQDWXUDOH]DSLHUGHQYDORUYLVXDOHQEHQHÀFLRGHRWUDV
TXHVHKDFHQLPSHUGLEOHVHQHOPRPHQWRGHSHUFLELU\UHFRQRFHU
ORV REMHWRV $O LJXDO TXH OD GLVFULPLQDFLyQ GHO FRQWUDVWH HQ HO
SURFHVRYLVXDOQXHVWURFHUHEURWLHQGHDVLPSOLÀFDUODVVHxDOHV
YLVXDOHVTXHUHFLEH(VWHHVHOSULQFLSLRSRUHOFXDOVHMXVWLÀFDQ
217&'B'/.17&0).+/17&)*145/+417&'-&4'.'*,+-%4%7&/1,)17+/+1-'7&
HQODVTXHODGRPLQDQWHUHDOQRHVXQDVLQRGRVRPiV
(Q HO GLEXMR FDGD OtQHD WLHQH XQD IXHU]D SURFHGHQWH GH OD
GLUHFFLyQTXHH[SUHVDVXLQWHQFLRQDOLGDG(OGLEXMDQWHKiELOVDEH
TXHSXHGHGLULJLUODPLUDGD\FRQHOODODDWHQFLyQGHOHVSHFWDGRU
KDFLD XQ SXQWR GHWHUPLQDGR FRQ VyOR KDFHU FRQYHUJHU YDULRV
YHFWRUHVGHIXHU]DIRUPDOTXHFRQVWLWX\HQHOMXHJRGHOtQHDV$XQ
FXDQGRHQXQFXDGURQRDSDUH]FDQH[SUHVDGDVODVOtQHDVGLEXMR
HVWUXFWXUDOHV QR ODV YHPRV FRPR WDOHV HQ OD QDWXUDOH]D VLQR
FRPRGLIHUHQFLDGHFRQWUDVWHVXE\DFHQHVFRQGLGDVRUGHQDQGR
ODVPDVDVODVOXFHV\ODVVRPEUDV
1LFRODV %RXUULDXG VRVWLHQH TXH ´HO DUWH HV OD RUJDQL]DFLyQ GH
SUHVHQFLD FRPSDUWLGD HQWUH REMHWRV LPiJHQHV \ JHQWHµ SHUR
WDPELpQ´XQODERUDWRULRGHIRUPDVYLYDVTXHFXDOTXLHUDSXHGH
DSURSLDUµ /D REUD GH DUWH FRQWHPSRUiQHD HV HQ Vt PLVPD XQ
LQWHUVWLFLR VRFLDO TXH FRPSRQH OD FXOWXUD (Q OD DFWXDOLGDG VH
FRQVLGHUD YLWDO ODV LQWHUUHODFLRQHV SHUVRQDOHV /DV SURSXHVWDV
DGRSWDQ PRGHORV GH RUJDQL]DFLyQ UHQRYDGRV WUDQVPLVLEOHV DO
JUDQS~EOLFR\VRFLDOHVSXGLHQGRWUDVODGDUVHDODYLGDFRWLGLDQD
(OUHFHSWRUFRPRVXMHWRSDVLYRSLHUGHHOLQWHUpVHQFRQVHFXHQFLD
##$
SDVDDXQDDFWLYLGDGRGLVFXUVRHQHOTXHVHDSURSLDLQWHUÀHUH
UHODFLRQD R GLDORJD FRQ OD SURSXHVWD 3DUD %RXUULDXG OD
DFWLYLGDGDUWtVWLFDHVXQVLVWHPDTXHSUHFLVDGHODSDUWLFLSDFLyQ
GHOUHFHSWRUQR\DSDUDDGTXLULUVHQWLGRVLQRLQFOXVRSDUDH[LVWLU
/DREUDFDUHFHGHHVHQFLDHQVtVRODQRHVXQREMHWRVLQRPiV
ELHQXQD´GXUDFLyQµHOWLHPSRHQTXHVHSURGXFHHOHQFXHQWUR
(QFXDQWRDORUHODFLRQDOHVWitQWLPDPHQWHOLJDGRDODDFFLyQ\
DO PLVPR WLHPSR FRPSRUWD XQ FXHVWLRQDPLHQWR GH ORV OtPLWHV
HQWUHHOHVSDFLR\HOWLHPSRHQHODUWH
<D QR VH SXHGH FRQVLGHUDU OD REUD FRQWHPSRUiQHD FRPR
XQHVSDFLRDUHFRUUHU/DREUDVHSUHVHQWDDKRUDPiVELHQ
FRPR XQD ´GXUDFLyQµ TXH GHEH VHU YLYLGD FRPR XQD
DSHUWXUDDODGLVFXVLyQLOLPLWDGD89
1R VH WUDWD SRU WDQWR GH FUHDU QXHYRV FDQDOHV R WHQGHQFLDV
DUWtVWLFDVVLQRGHJHQHUDUFRQWH[WRVRVLWXDFLRQHVTXHSHUPLWDQ
UHFXSHUDU OR FRWLGLDQR OD HVHQFLD YLYD GHO KRPEUH QXHVWUD
FRQGLFLyQXELFDGDHQHOHVSDFLRWLHPSRFRQWLQXR(VRVFRQWH[WRV
R VLWXDFLRQHV SXHGHQ VHU FRQVWUXFFLRQHV DUTXLWHFWXUDV HQ ODV
FXDOHVHOHVSHFWDGRUVHFRQYLHUWHHQXVXDULRRSDUWLFLSDQWH
$TXtHODUWLVWDGLItFLOPHQWHPDQWLHQHODDXWRULGDGVREUHOD
H[SHULHQFLDUHDOTXHVHGHVSOLHJDHQHODFRQWHFLPLHQWRDVt
TXHPHMRUOODPDUORXQVLPSOHRUTXHVWDGRUGHVLWXDFLRQHV
GHO PLVPR PRGR HO HVSHFWDGRU WDPSRFR HVWi OODPDGR D
VXIULU OD FRQYHQFLRQDO SDVLYLGDG GH OD H[SHFWDFLyQ VLQR
TXH SUHFLVDPHQWH DO FRQWUDULR VH UHTXLHUH VX SUHVHQFLD
SDUDTXHHODFRQWHFLPLHQWRFUH]FD\VHGHVDUUROOHJUDFLDVD
VXDFFLyQHQFDOLGDGGHXVXDULRGHODDUTXLWHFWXUDSDUDHO
DFRQWHFLPLHQWRSXHVWDDVXGLVSRVLFLyQ88
Relación espacio – tiempo. Evolución en el arte
(QWHQGHPRV DO HVSDFLR FRPR HO FRQWLQHQWH GH P~OWLSOHV \
GLYHUVDVIRUPDVGHH[SUHVLyQFXOWXUDOH[SUHVLRQHVTXHWUDGXFHQ
ODVFRQFHSFLRQHVVREUHHOHQWRUQRTXHSRVHHXQJUXSRKXPDQR
!!"
GHWHUPLQDGR (O HQWRUQR GHSHQGHUi GHO KRPEUH HVWDUi
VXSHGLWDGRDpO/DFRQVWUXFFLyQGHOHVSDFLRFUHHPRVWDPELpQ
VH UHDOL]D PHQWDOPHQWH PHGLDQWH OD DVLPLODFLyQ \ DSUHKHQVLyQ
GHXQHVSDFLR\VXXVRKDELWXDOXVRTXHFUHHPRVUHVSRQGHD
QHFHVLGDGHVFRJQLWLYDV
/DFRQFHSFLyQGHOHVSDFLRDORODUJRGHORVWLHPSRVKDYHQLGRD
FRQVLGHUDUVHGHGLVWLQWDVIRUPDVGHVGHODDQWLJHGDGVHHQWHQGtD
FRPROXJDUSODQRHQHOTXHKDELWDEDQORVREMHWRVORVOtPLWHVHUDQ
LQÀQLWRVHQJHRPHWUtDHXFOLGLDQD\SDUDHQWHQGHUHQODpSRFDORV
/1-/').17&4'&*')*'7'-.%/+0-&'7)%/+%2&'*%&-'/'7%*+1&%)1;%*7'&'-&
ODVPDWHPiWLFDVFRQFUHWDPHQWHHQODJHRPHWUtDGHODpSRFD(O
WUDWDPLHQWRGHOHVSDFLRHQJHRPHWUtDQRFRQVLGHUDEDYLQFXODQWH
HOWLHPSR\DTXHQLWDQVLTXLHUDHUDHQVtXQDGLPHQVLyQVLQR
DOJR TXH VLHPSUH HVWXYR SUHVHQWH HQ WRGDV ODV FRVDV 3RU HOOR
HUD LQYDULDQWH \ XQLIRUPH \ SRU OR WDQWR QR SDUWLFLSDED FRPR
SURWDJRQLVWDHQHOHVWXGLRGHODUHSUHVHQWDFLyQGHOHVSDFLR
(VXQKHFKRSUREDGRTXHHOWLHPSRVHGHEHDXQHVSDFLRTXH
ORMXVWLÀFDSHURKHPRVWDUGDGRVLJORVHQDFHSWDUTXHWUDWDUHO
'7)%/+1& 7+-& *'2%/+1-%*21& /1-& '2& .+',)1& '7& 5-%& +-/1C'*'-/+%& .%2&
FRPR KDEODU GH OD OX] VLQ FRQWUDSRQHU OD REVFXULGDG 6L KDVWD
ÀQDOHVGHOVLJOR;,;VHFRQVLGHUDEDQSRUVHSDUDGRKR\VHDFHSWD
SRU GHPRVWUDFLyQ HPStULFD TXH DPERV WLHQHQ XQD UHODFLyQ
GLUHFWD $Vt TXH GHVGH PL SHUVSHFWLYD FRQVLGHUR TXH KHPRV
LGRKHUHGDQGR\GDQGRSRUFLHUWDVORTXHKR\SDUHFHQVRPEUDV
GHO SDVDGR GH OD KLVWRULD GH OD FLHQFLD (V QHFHVDULR DGTXLULU
FRQFLHQFLDV UHQRYDGDV GHO PXQGR TXH FRQRFHPRV VLQ ROYLGDU
HOODVWUHGHODVKLVWRULDSHURDFWXDOL]iQGRVH\SRVLFLRQiQGRQRV
HQHOPXQGRUHDO\SUHVHQWH(VFLHUWRTXHORVSDUiPHWURVKDQ
FDPELDGRVXEVWDQFLDOPHQWH\HOORKDGHVFXELHUWRJUDQGHVHUURUHV
GHDSUHFLDFLyQHQHOFDPSRGHODUWHGHOVLJOR;;WDQFRQYXOVR
FRPR DUELWUDULR FRQ PRGHORV DMHQRV D OD H[SHULHQFLD HVWpWLFD
YLWDO &ODUDPHQWH VH UHFODPDQ FULWHULRV \ SDUiPHWURV GHÀQLGRV
HQIXQFLyQGHOWLHPSR\QRPHUHÀHURDXQWLHPSRGHUHORMVLQR
GHH[SHULHQFLDHVWpWLFDVRFLDO
&RQ HVWR TXLHUR GHFLU TXH KR\ FUHHPRV HQ OD YDULDELOLGDG GHO
HVSDFLRHQWRGRVVXVQLYHOHVWUDGXFLGRHQDTXHOODFRQFHSFLyQ
##$
TXHWXYLHURQGHOPXQGRORVGLYHUVRVJUXSRVKXPDQRVTXLHQHV
VH DSURSLDURQ GHO PHGLR OR DVLPLODURQ \ DVXPLHURQ FRPR
HQWRUQR H[LVWHQFLDO 'LFKR HQWRUQR H[LVWHQFLDO GHOLPLWDGR
SRU OD SHUFHSFLyQ \ FRQFHSFLyQ SURSLD GH OD UHODFLyQ KRPR
)%+7%F'& '()*'7%4%& ,'4+%-.'& 2%& .*%-7,+7+0-& 4'& 2%7& +4'%7& C'/C%7&
WDQJLEOHVSRUODFRQGLFLyQGHO´KRPRµFRPRFUHDGRUGHREMHWRV
\ PRGXODGRU GH SDLVDMHV &XDQGR KDEODPRV GH WUDQVPLVLyQ
QRV UHIHULPRV DO SURFHVR SRU HO FXDO VH WUDQVPLWHQ GLYHUVDV
FRQVWUXFFLRQHVPHQWDOHV
/LQR &DEH]DV VRVWLHQH OD YLQFXODFLyQ HQWUH HO PHGLR GH
WUDQVPLVLyQ FRPR HV HO DUWH HQ FRQFUHWR HO GLEXMR FRQ ODV
FLHQFLDVXQDUHODFLyQTXHVLHPSUHKDHVWDGRSUHVHQWH
FRQ IUHFXHQFLD DUWH \ GLEXMR VH FRQVLGHUDQ WpUPLQRV
SUiFWLFDPHQWH VLQyQLPRV 7DPELpQ VH VXHOH SHQVDU HQ HO
GLEXMR FRPR XQ JpQHUR R XQD IRUPD SDUWLFXODU GH DUWH
1R REVWDQWH DXQTXH HO GLEXMR HQ JHQHUDO VH OH DWULEX\D
XQD YLQFXODFLyQ SULQFLSDO FRQ HO DUWH WDPELpQ SXHGH
UHODFLRQDUVHFRQRWURViPELWRVGHODFXOWXUDHQWUHORVTXH
VHHQFXHQWUDQODFLHQFLD\ODWHFQRORJtD8:
7HRUtDVFRPROD5HODWLYLGDGOD)tVLFD&XiQWLFDHO3ULQFLSLRGH
,QFHUWLGXPEUH\OD7HRUtDGHO&DRVFRQVWLWX\HQXQLQVWUXPHQWDO
WHyULFRPHWRGROyJLFRPX\YDOLRVRSDUDORVDUWLVWDV\FLHQWtÀFRV
GHKR\/DUHODWLYLGDGGHORVFRQFHSWRV¢7LHQHVHQWLGRFXDOTXLHU
DÀUPDFLyQ"&RQHVWDSUHJXQWDLQLFLDQVXOLEUR¢4XpHVODWHRUtD
GH OD UHODWLYLGDG" / /DQGDX \ < 5XPHU $OEHUW (LQVWHLQ
GHVFXEULGRUGHODV7HRUtDV(VSHFLDO\*HQHUDOGHOD5HODWLYLGDG
GHPRVWUy FRPR FRQFHSWRV FRPR GHUHFKD H L]TXLHUGD VRQ
UHODWLYRV SRU HMHPSOR FXDQGR QRV PLUDPRV HQ XQ HVSHMR
GHEHPRVUHIHULUQRV¢DTXHGHUHFKD"¢ODGHOHVSHMRRODQXHVWUD"
(V LPSRVLEOH GDU XQD UHVSXHVWD GH IRUPD LQPHGLDWD 6L QRV
PRYHPRVKDFLDHOQRUWHHOODGRGHUHFKRVHULDHOHVWH\HOL]TXLHUGR
HO RHVWH SRU HO FRQWUDULR VL OR KDFHPRV KDFLD HO VXU HO RHVWH
VHUiQXHVWUDGHUHFKD9HPRVHQWRQFHVTXHSDUDUHIHULUQRVDORV
FRQFHSWRVGHL]TXLHUGD\GHUHFKDGHEHPRVWHQHUHQFXHQWDXQ
!!"
UHIHUHQWHUHVSHFWRDOFXDOGHÀQLPRVODGHUHFKDRODL]TXLHUGD/R
DQWHULRUQRVLQGLFDTXHORVFRQFHSWRV´GHUHFKDµH´L]TXLHUGDµVRQ
UHODWLYRV &RQ RWUDV SDODEUDV ORV FRQFHSWRV DGTXLHUHQ VHQWLGR
~QLFDPHQWH GHVSXpV GH KDEHU GHÀQLGR OD GLUHFFLyQ UHVSHFWR D
ODFXDOVHDSOLFDODDÀUPDFLyQ/RGLFKRDQWHULRUPHQWHWDPELpQ
VHDSOLFDSDUDHOWLHPSR\HOHVSDFLR1RWLHQHVHQWLGRKDEODUGH
WLHPSRVLQSUHFLVDUXQDORFDOL]DFLyQSUHYLD
/DUHODWLYLGDGGHOPRYLPLHQWRTXHHVWDPRVREVHUYDQGRGHSHQGH
GHOOXJDU³HVSDFLR\YHORFLGDG³HQTXHQRVHQFRQWUDPRV7RGDV
QXHVWUDVDFFLRQHVHVWiQPDUFDGDVSRUHOWLHPSR\HOHVSDFLR
(V XQD QXHYD UHDOLGDG PX\ GLVWLQWD D OD TXH KDVWD HQWRQFHV
LPSHUDED OD UHDOLGDG QHZWRQLDQD HO WLHPSR LQGHSHQGLHQWH GHO
HVSDFLR(QVXVI+910989:$K:*"#C:*90:,VDDF1HZWRQQRVRIUHFH
HOSULPHUPRGHORPDWHPiWLFRGHVDUUROODGRSDUDHOWLHPSR\HO
HVSDFLR(QVXPRGHOR1HZWRQQRVSUHVHQWDHOWLHPSR
\HOHVSDFLRHQIRUPDVHSDUDGD\ORVVXFHVRVVHUHDOL]DEDQVREUH
HOORVSHURVLQTXHHVWRVVXFHVRVORVDIHFWDUD(OWLHPSRHVWDED
UHSUHVHQWDGRSRUXQDOtQHDUHFWDLQÀQLWDHQDPEDVGLUHFFLRQHV
\DGHPiVKDEtDH[LVWLGRVLHPSUH\H[LVWLUiVLHPSUHHVGHFLUHO
WLHPSRHUDFRQVLGHUDGRHWHUQR/DWHRUtDJHQHUDOGHODUHODWLYLGDG
GH(LQVWHLQDÀUPDFRQWUDULRDORTXH1HZWRQSHQVDED
TXHHOHVSDFLRWLHPSRHVWiGHIRUPDGR\GLVWRUVLRQDGRGHELGRD
ODGLVWULEXFLyQGHPDWHULD\HQHUJtDHQHOXQLYHUVRSRUORTXH
\D QR HV SODQR 3RU OR WDQWR ORV REMHWRV TXH VH PXHYHQ HQ HO
HVSDFLRWLHPSR DXQTXH LQWHQWDQ KDFHUOR GH PDQHUD UHFWLOtQHD
VLJXHQXQDWUD\HFWRULDFXUYDGD/DGLVWDQFLDPiVFRUWDHQWUHGRV
SXQWRV \D QR HV OD UHFWD VHJ~Q OD JHRPHWUtD HXFOLGLDQD VLQR
OD JHRGpVLFD 3DUHFH TXH VX PRYLPLHQWR VH YH DIHFWDGR SRU OD
DFFLyQGHODJUDYHGDG(OWLHPSR\HOHVSDFLRHQODWHRUtDGHOD
UHODWLYLGDGHVWiQHQWUHOD]DGRVHVLPSRVLEOHVHSDUDUORVQRH[LVWH
HO WLHPSR DEVROXWR FDGD REVHUYDGRU WLHQH VX SURSLR WLHPSR \
HVWHWLHPSRSHUVRQDOHVYDULDEOH
+HPRV PHQFLRQDGR TXH (LQVWHLQ VXVWLWX\y HO WLHPSR OLQHDO
SRU RWUR PiV ÁXLGR XQ WLHPSR TXH VH H[SDQGH R VH FRQWUDH
GHSHQGLHQGRGHODVLWXDFLyQGHODVSHUVRQDV´3RQWXPDQRµ³
##$
GHFtD(LVQWHLQ³HQXQKRUQRFDOLHQWHGXUDQWHXQPLQXWR\WH
SDUHFHUiXQDKRUD6LpQWDWHMXQWRDXQDFKLFDSUHFLRVDGXUDQWH
XQDKRUD\WHSDUHFHUiXQPLQXWR(VRHVODUHODWLYLGDG
6L HVWiV DEXUULGR HO WLHPSR QR SDVD QXQFD VL HVWiV
GHVHVSHUDGR VH WH DFDED HO WLHPSR VL HVWiV OOHQR GH
HQWXVLDVPR HO WLHPSR YXHOD FXDQGR WH HQDPRUDV HO
WLHPSRVHGHWLHQH(QRWUDVSDODEUDVFDGDYH]TXHWRPDV
XQDDFWLWXGFRQUHVSHFWRDOWLHPSRHQUHDOLGDGH[SUHVDV
DOJRVREUHWLPLVPR(OWLHPSRHQXQVHQWLGRVXEMHWLYR
HVXQHVSHMR8<
/DVPDWHPiWLFDVDPHQXGRUHTXLHUHQUHSUHVHQWDUGDWRV\FyPR
pVWRV YDUtDQ FRQ HO WLHPSR 3DUD HOOR ORV PDWHPiWLFRV KDQ
HODERUDGR PXFKDV QRFLRQHV GH ¶HVSDFLR· YLQLHQGR D VHU FRPR
´DOPDFHQHVµGHHVRVGDWRVHQPRYLPLHQWR&DGDHVSDFLRSHUPLWH
DVt UHJLVWUDU FyPR VH PXHYHQ ORV FXHUSRV GH FyPR FDPELD
OD VLWXDFLyQ (Q OD FLHQFLD HO HVSDFLR GH IDVHV HV XQ WpUPLQR
XWLOL]DGRSDUDGHVFULELUHOHVSDFLRGHWRGDVODVSRVLELOLGDGHVHQ
XQD VLWXDFLyQ GDGD 8Q PRYLPLHQWR HV GHVFULWR HQWRQFHV FRQ
OR TXH VH GHQRPLQD XQ FDPLQR HQ HVWH HVSDFLR QR HO FDPLQR
XVXDOTXHQRVRWURVUHFRUUHUtDPRVVLQRXQDVHULHGHSRVLFLRQHV
TXHGHVFULEHQHOPRYLPLHQWRRHOFDPELRSURGXFLGRGXUDQWHXQ
SHULRGRGHWLHPSR8QHMHPSORSRGUtDPRVREVHUYDUORHQQXHYDV
LQYHVWLJDFLRQHV VREUH HO GLEXMR \ VX UHODFLyQ WULGLPHQVLRQDO
FRPRHODUWtFXORWLWXODGR´'LEXMDQGRREMHWRV'HQHODLUHµ8=&
(QHOFXDOFLHQWtÀFRVGHODFRPSXWDFLyQFRPRVRQ'DQLHO.HHIH
5REHUW=HOH]QLN\'DYLG/DLGODZGH%URZQ8QLYHUVLW\FUHDURQ
XQDWHFQRORJtDTXHSHUPLWHJHQHUDUREMHWRV'HQHODLUHFRQOD
D\XGDGHXQDPDVFDUDGHUHDOLGDGYLUWXDOXQDDJXMD\XQREMHWR
GH UDVWUHR (VWD WHFQRORJtD LQWURGXFH GRV QXHYDV HVWUDWHJLDV
XVDU FXDOTXLHUD GH ODV PDQRV XQD R ODV GRV 3URSRUFLRQD D
ORV DUWLVWDV ODV KHUUDPLHQWDV QHFHVDULDV SDUD GLEXMDU GLIHUHQWHV
WLSRVGHFXUYDVSDUDYHU\HGLWDUVXWUDEDMR&RQHVWHVLVWHPDHO
DUWLVWDWRPDXQDDJXMDHQXQDPDQRSDUDGLEXMDU\XQUDVWUHDGRU
HQODRWUDPDQRSDUDGHÀQLUODGLUHFFLyQGHODOtQHD(ODUWLVWD
FRRUGLQDORVPRYLPLHQWRVFRQDPEDVPDQRVSDUDH[DPLQDUVX
WUDEDMRGHVGHGLIHUHQWHViQJXORVDFRUGHVFRQHOGLEXMR
!!"
0DUWtQ3UDGDHQ´/DVLQVWUXFFLRQHVGHOVRIWZDUH\GHOKDUGZDUH
FRPR QXHYRV PDQXDOHV GH GLEXMRµ QRV SUHVHQWD XQD QXHYD
ySWLFDXQDQXHYDYLVLELOLGDGTXHYDPiVDOOiGHOSODQRGHXQD
SDQWDOODGHFRPSXWDGRU
/D ySWLFD GHO PHGLR WUDWD GH UHFXSHUDU DTXHO FDUiFWHU
HQYROYHQWHGHODLPDJHQFRPRHQWRUQRTXHSUHWHQGLHURQ
ORV SDQRUDPDV GHO VLJOR ;,; \ ORV SULPHURV WHDWURV
ySWLFRVEDVDGRVHQODSUR\HFFLyQGHWUDQVSDUHQFLDVVREUH
XQD SDQWDOOD FRQWLQXD FLUFXODU \ HQYROYHQWH 3UHWHQVLyQ
VLPLODUDODGHODVQXHYDVIRUPDVGHODUHDOLGDGYLUWXDOHQ
ODVTXHXQDVJDIDVDQWHVHOPHGLRFRUUHFWRUGHODYLVLyQ
FRLQFLGHQDKRUDFRQHOREMHWR\HOHQWRUQRTXHHVSHUFLELGR
WUDVIRUPiQGRVHHQHOPHGLRGHDFFHVRDRWUDUHDOLGDG/RV
RMRVTXHHVWiQWUDVHOODVQRPLUDQPiVDOOiGHOFULVWDO«
/D SpUGLGD GH OD SHUVSHFWLYD HXFOLGLDQD \ OD GH OD
RUJDQL]DFLyQ GH OD GLVWDQFLD TXH GH HOOD GHSHQGtD OD
FRQYLHUWH HQ XQD ySWLFD WiFWLO 1R HV H[WUDxR TXH WUDV
ORV RMRV OD PDQR IXHUD OD VLJXLHQWH SDUWH GHO FXHUSR HQ
LQFRUSRUDUVHDODH[SHULHQFLDGHOPXQGRYLUWXDODWUDYpVGH
ODHQYROWXUDGHO´GDWDJOREHµ
(QODJHRPHWUtDHXFOLGHDQDVHGHVFULEtDHOHVSDFLRFRPR~QLFR
\ SODQR &RQ 'HVFDUWHV DxDGLHQGR OD GLPHQVLyQ GHO WLHPSR
UHORM HQ HO SURSLR VLVWHPD GH UHIHUHQFLD FDUWHVLDQR HV GHFLU
[\]W UHORM REWHQGUtDPRV OR TXH KDVWD SULPHURV GHO VLJOR
;;VHFRQFHEtDFRPRUHODFLyQHVSDFLRWLHPSRRORTXHVHULD
ORPLVPRHOPRYLPLHQWRHQHOHVSDFLRJHQpULFR7HRUtDVFRPR
OD*HQHUDOGHOD5HODWLYLGDGDQWHVPHQFLRQDGDRODGHFDPSRV
XQLÀFDGRVURPSHQFRQORVSULQFLSLRVGHUHIHUHQFLDWUDGLFLRQDOHV
%iVLFDPHQWHODGLVWDQFLDPiVFRUWDHQWUHGRVSXQWRVQRHVXQD
UHFWDVLQRODJHRGpVLFD(VGHFLUODUHFWDHVHOVHJPHQWRPtQLPR
GHXQDFXUYDRORTXHVHUtDORPLVPRODUHFWDHVXQSURGXFWR
ÀFWLFLR6LFRQVLGHUDPRV\DFHSWDPRVDPEDVWHRUtDVHOVHQWLGR
GHUHFWDFDPELDGHELGRDVXUHODFLyQFRQHOWLHPSR\HO´SODQRµ
GRQGHVHGHVDUUROOD'LFKRSODQRDQiORJDPHQWHVXIULUtDHOPLVPR
HIHFWR3RUWDQWRODFXUYDWXUDGHOSODQRSURYRFDTXHODGLVWDQFLD
##$
PiV FRUWD HQWUH GRV SXQWRV QXQFD VHD XQD UHFWD ,PDJLQHPRV
XQDVHPLHVIHUDHOSODQRHVXQDSUR\HFFLyQGHODFXUYD
Fig. 2. Proyección en un plano.
3RUHOORODGHÀQLFLyQGHUHFWDHQXQSODQRVLHPSUHHVWDUiUHIHULGD
DOSXQWRGHYLVWDÀFWLFLRGHOREVHUYDGRUQXQFDDOSURSLRSODQR
/RV SDUiPHWURV GH UHIHUHQFLD TXH VH HVWDEOH]FDQ VRQ VLHPSUH
PRQRFXODUHVGLFKRGHRWUDIRUPDODVHQVDFLyQGHSURIXQGLGDG
HQHOVLVWHPDYLVXDOKXPDQRVHUHDOL]DPHGLDQWHODELQRFXODULGDG
FRQHOVRODSDPLHQWRGHGRVSXQWRVGHYLVWDGHXQDPLVPDLPDJHQ
FRQXQGHVSOD]DPLHQWRGHORVIRFRVGLVWDQFLDGRVHQSURSRUFLyQ
DO iQJXOR Pi[LPR GH SHUFHSFLyQ 6L HO iQJXOR HV PHQRU TXH
OD SHUVSHFWLYD GH LPDJHQ HVWD VLHPSUH VHUi UHFWD SRU HOOR HQ
VLVWHPDV GH UHIHUHQFLD FRUWRV QDWXUDOHV ODV OLQHDV ÀFWLFLDV VRQ
UHFWDVHOHUURUQRVGLVWUDHSRUTXHORVSDUiPHWURVUHIHUHQFLDOHV
HQORVTXHDSR\DUVHFDPELDQ
9HUGDGHUDPHQWHFUHRTXHHOSUREOHPDQRYDPiVDOOiGHORTXH
QXHVWURFHUHEURSHUFLEH\UHKDFH/DVJHRPHWUtDVQRVRQSODQDV
SHURKDQVLGRFRQVLGHUDGDVGHVGHHOSXQWRGHYLVWDÀMRGHTXLHQ
ODVGHÀQtDHQFDGDPRPHQWRGHODKLVWRULD(OWLHPSRHVUHODWLYR
QR TXLHUH GHFLU TXH SXHGD YDULDUVH HQ XQD OLQHD HQ HO HVSDFLR
SHUR VL ORV SDUiPHWURV GH UHIHUHQFLD FDPELDQ WDQWR HO WLHPSR
FRPRHOSODQRSRUWDQWRODOtQHDWDPELpQYDUtDLQH[RUDEOHPHQWH
/DVUHODFLRQHVHQWUH[\]VRQEiVLFDVSDUDKDEODUGHWLHPSR
6LQ HPEDUJR KHPRV DSUHQGLGR D WUDEDMDU PXWLODGRV GH DOJXQD
!!"
GH ODV GLPHQVLRQHV UHFWDV SODQRV \ YRO~PHQHV (Q OD TXH
QXQFD LQWHUIHUtD HO PRPHQWR WLHPSR (Q YHUGDG HQ HO SURSLR
VLVWHPD FDUWHVLDQR XQ SXQWR GH UHIHUHQFLD HQ HO HVSDFLR EL R
WULGLPHQVLRQDOHQVtPLVPRUHSUHVHQWDUtDXQODSVRGHWLHPSR
3HUR VL OD UHODWLYLGDG GHO HVSDFLRWLHPSR FDPELy OD PDQHUD
GH FRQFHELU HO PXQGR HO SULQFLSLR GH LQFHUWLGXPEUH IXH OD
FRQWULEXFLyQ PiV LPSRUWDQWH GH +HLVHQEHUJ D OD ItVLFD IXH
FRQRFLGRWDPELpQFRPRLQGHWHUPLQDFLyQIRUPXODGRHQ
\ SRU HO TXH REWXYR HO SUHPLR 1REHO GH )tVLFD HQ (O
SULQFLSLR GH LQFHUWLGXPEUH HVWDEOHFH TXH HV LPSRVLEOH UHDOL]DU
XQD GHWHUPLQDFLyQ H[DFWD \ VLPXOWiQHD GH OD SRVLFLyQ \ GHO
PRPHQWRGHXQFXHUSRDOPXOWLSOLFDUDPEDVLQGHWHUPLQDFLRQHV
VHREWHQtDODFRQVWDQWHGH3ODQN(VWHSULQFLSLRGHVWURQyODOH\
GH FDXVD \ HIHFWR TXH VH KDEtD DQFODGR HQ OD FLHQFLD GHVGH OD
pSRFDGH7DOHV\GHELOLWyODÀORVRItDGHWHUPLQLVWDGHOXQLYHUVR
$FWXDOPHQWH VDEHPRV TXH GHEHPRV PLUDU OD )tVLFD FRQ
´RMRVFOiVLFRVµVLVHWUDWDGHREMHWRVRVLWXDFLRQHVTXHQRV
VRQ FRWLGLDQDV \ SUy[LPDV SHUR TXH HVWD PLUDGD GHEH
FDPELDUVH D ´UHODWLYLVWDµ SDUD JUDQGHV YHORFLGDGHV \ D
´FXiQWLFDµSDUDGLPHQVLRQHVDWyPLFDV8>
(O REVHUYDGRU LQWHUDFW~D FRQ HO VLVWHPD GH WDO PDQHUD TXH HO
VLVWHPD QR WLHQH XQD H[LVWHQFLD LQGHSHQGLHQWH WHQHPRV XQ
FRQRFLPLHQWROLPLWDGRORTXHXQHOHFWUyQHVWiKDFLHQGRFXDQGR
ORHVWDPRVREVHUYDQGRSHURQRVDEHPRVQDGDGHORTXHHVWi
KDFLHQGRFXDQGRQRORREVHUYDPRV1DGDHVUHDODPHQRVTXH
ORREVHUYHPRV<DHQHOVLJOR;9,,HORELVSRGH&OR\QH,UODQGD
*HRUJH %HUNHOH\ OR KDEtD UHFRQRFLGR FXDQGR DÀUPy VHU HV
VHU SHUFLELGR (O SULQFLSLR GH LQFHUWLGXPEUH ERUUy OD IURQWHUD
HQWUHHOREVHUYDGRU\ORREVHUYDGRHOSULQFLSLRGHREMHWLYLGDG
GHODFLHQFLD2QGD\SDUWtFXODH[LVWHQHQXQDVXSHUSRVLFLyQGH
HVWDGRV
3DUD +DZNLQJ OD PHGLFLyQ FDPELD OD UHDOLGDG XQD OH\ GH OD
QDWXUDOH]D
##$
/D UHDOLGDG REMHWLYD ³GLFH +HLVHQEHUJ³ VH KD
HYDSRUDGR\ORTXHQRVRWURVREVHUYDPRVQRHVODQDWXUDOH]D
HQ Vt VLQR OD QDWXUDOH]D H[SXHVWD D QXHVWUR PpWRGR GH
LQWHUURJDFLyQ
(VWR VLJQLÀFD TXH OD UHDOLGDG TXH SRGHPRV REVHUYDU HVWi
FRQGLFLRQDGD D ODV FDUDFWHUtVWLFDV GHO REVHUYDGRU HV SUREDEOH
TXH SDUD FDSWDU OD UHDOLGDG TXH SHUFLELPRV WHQJDPRV TXH VHU
FRPRVRPRV
(Q HO XQLYHUVR WRGR VH FRQHFWD FRQ WRGR XQ HOHPHQWR GH OD
UHDOLGDGRXQDVXEWRWDOLGDGWLHQHODLQIRUPDFLyQGHOWRGR(VWRHV
ORTXHQRVH[SOLFDHOKRORJUDPDLQYHQWDGRSRUHOItVLFREULWiQLFR
GHRULJHQK~QJDUR'HQQLV*DERU\SRUORTXHREWXYRHOSUHPLR
1REHOGH)tVLFDHQ
(OWpUPLQRKRORJUDPDVHGHULYDGHODVSDODEUDVJULHJDVKRORVTXH
VLJQLÀFDFRPSOHWRRLQWHJUDO\JUDPDUHJLVWUR8QKRORJUDPDHV
XQDLPDJHQWULGLPHQVLRQDOIRWRJUDÀDGDGHODUHDOLGDGXWLOL]DQGR
XQUD\ROiVHU(VWDLPDJHQKRORJUiÀFDHVXQDUHSUHVHQWDFLyQWDQ
H[DFWD\QtWLGDHQVXVGHWDOOHVGHXQRULJLQDOSHUVRQDV\REMHWRV
HQWHUFHUDGLPHQVLyQDXQTXHFRQIRUPDGRSRUKDFHVGHOX]TXH
LQFOXVRSXHGHUHHPSOD]DUDORULJLQDOPLVPR/D~QLFDGLIHUHQFLD
HQWUHHOKRORJUDPD\HORULJLQDOHVTXHDHVWH~OWLPRVHSXHGH
WRFDU\DOKRORJUDPDQR6LVHSDUWHHVWDLPDJHQSRUODPLWDG
HQFDGDPLWDGDSDUHFHODLPDJHQWULGLPHQVLRQDOFRPSOHWDVLVH
FRQWLQ~DSDUWLHQGRVLQLPSRUWDUODVYHFHVTXHVHKDJDFDGDSDUWH
SUHVHQWDODLPDJHQFRPSOHWD\WULGLPHQVLRQDOGHODRULJLQDO
([LVWHXQDYDULHGDGGHKRORJUDPDV1RVUHIHULUHPRVDGRVWLSRV
KRORJUDPDVGHFRPSRVLFLyQ\ORVGHQRPLQDGRVDUFRLULV/RVGH
FRPSRVLFLyQSXHGHQPRYHUVH\ORVDUFRLULVTXHGHSHQGLHQGRGH
ODSRVLFLyQGHOREVHUYDGRUSHUPLWHQSHUFLELUGLYHUVRVFRORUHV
.DUO 3ULEDP XQ QHXURÀVLyORJR LQYHVWLJDGRU GHO &HQWUR GH
(VWXGLRV$YDQ]DGRV\GHODV&LHQFLDVGHO&RPSRUWDPLHQWRGH
OD8QLYHUVLGDGGH6WDQIRUG&DOLIRUQLDHODERUyDSULQFLSLRVGH
ORVDxRVXQDWHRUtDKRORJUiÀFDGHOIXQFLRQDPLHQWRFHUHEUDO
HO 0RGHOR +RORJUiÀFR GHO &HUHEUR (V XQ PRGHOR FXiQWLFR
!"#
TXH RIUHFH XQD H[SOLFDFLyQ GH ORV SURFHVRV GHQGUtWLFRV \
QDQRQHXUROyJLFRVTXHSURGXFHQODSHUFHSFLyQHQORVLQGLYLGXRV
3DUD 3ULEDP8? HO FHUHEUR HV XQD HQWLGDG KRORJUiÀFD TXH
LQWHUSUHWDXQXQLYHUVRKRORJUiÀFR\TXHHOHVSDFLRHOWLHPSRORV
REMHWRV\ODUHDOLGDGH[WHULRUPLVPDVRQFUHDGRVSRUHOFHUHEUR
.DUO 3ULEDP \ 'DYLG %RKP8# GH OD 8QLYHUVLGDG GH /RQGUHV
SODQWHDQTXHQXHVWURVFHUHEURVFRQVWUX\HQPDWHPiWLFDPHQWHOD
UHDOLGDGFRQFUHWDDWUDYpVGHODLQWHUSUHWDFLyQGHIUHFXHQFLDVGH
RWUDGLPHQVLyQTXHWUDVFLHQGHHOWLHPSR\HOHVSDFLR(VPX\
SRVLEOHGLFHQTXHSDUDSRGHUYHURtUROHUHWFHOFHUHEURUHDOL]D
FRPSOLFDGRVFiOFXORVHQUHODFLyQDODIUHFXHQFLDGHORVGDWRVTXH
SHUFLEHGXUH]DFRORURORU
6LVHDFHSWDODLQWHUSUHWDFLyQGHORV´PXQGRVP~OWLSOHVµHQWRQFHV
SRUFDVXDOLGDGQRVRWURVYLYLPRVHQXQRGHHVWRVXQLYHUVRV\
HQORVRWURVHVPX\SRVLEOHTXHH[LVWDQYHUVLRQHVGHQRVRWURV
PLVPRVH[LVWHQP~OWLSOHVKLVWRULDVHOXQLYHUVRVHGHVGREOHHQ
GRV YHUVLRQHV GH Vt PLVPR (VWH GHVGREODPLHQWR FRQVWDQWH GH
PXQGRV VH EDVD HQ XQDV HFXDFLRQHV PDWHPiWLFDV LQREMHWDEOHV
HQODLGHDGHTXHWRGDODHYROXFLyQWHPSRUDOYLHQHGDGDSRUOD
HFXDFLyQ GH 6FKU|GLQJHU YHU SRU HMHPSOR )UDQN - 7LSOHU:9
/DLQWHUSUHWDFLyQGHODWHRUtDGHORVPXQGRVP~OWLSOHVQRVGLFH
TXH OR ~QLFR TXH FRQRFHPRV HV HO SDVDGR TXH QR FRQRFHPRV
HO SUHVHQWH HQ WRGRV VXV GHWDOOHV \ TXH HO IXWXUR QR HVWi
GHWHUPLQDGRSXHVWRTXHKD\PXFKDVUXWDVPXFKRVPXQGRVTXH
QRVFRQGXFHQDOIXWXUR\DOJXQDYHUVLyQGHQRVRWURVVHJXLUiSRU
HOODV&DGDXQDGHHVWDVYHUVLRQHVGHQRVRWURVPLVPRVFUHHUiTXH
DYDQ]DDWUDYpVGHO~QLFRFDPLQR\VHPLUDUiHQ~QLFRSDVDGR
SHURUHVXOWDDEVROXWDPHQWHLPSRVLEOHFRQRFHUHOIXWXURSRUTXH
KD\LQÀQLGDGGHHOORV1RVRWURVWDPELpQGHEHPRVGHH[LVWLUHQ
PXFKRVHVWDGRVVLPXOWiQHDPHQWHDXQTXHQRQRVGHPRVFXHQWD
'HEHQ H[LVWLU PXFKDV YHUVLRQHV GH XQR PLVPR GH OD WLHUUD \
GHO XQLYHUVR FRPSOHWR WRGRV ORV HYHQWRV SRVLEOHV WRGDV ODV
YDULDFLRQHVFRQFHELEOHVGHQXHVWUDVH[LVWHQFLDV1RYLYLPRVHQ
XQXQLYHUVR~QLFRVLQRHQXQYDVWRPXOWLYHUVR
(QODWHRUtDGHOFDRVH[LVWHQWUHVFRQFHSWRVFODYHWUDQVYHUVDOHVHO
FRQWUROODFUHDWLYLGDG\ODVXWLOH]D(OFRQWUROODLQFHUWLGXPEUH\
##$
ODFRQWLQJHQFLDVRQIHQyPHQRVTXHDFRPSDxDQDODUWLVWDWRGDOD
YLGDEXVFDQGRVLHPSUHPDQHUDVGHHQIUHQWDUVH\GHHOLPLQDUOD
(O DUWLVWD VLHPSUH VH KD HQIUHQWDGR D OD LQFHUWLGXPEUH GH
OD UHSURGXFFLyQ GH OD LPDJHQ UHDO DQWHV \ DKRUD D OD UHODFLyQ
WUDQVPLVLEOH GHO FRQFHSWR \R LGHD KDVWD OD REUD WDQJLEOH R
SHUFHSWLEOH (Q HO SURFHVR FUHDWLYR VLHPSUH VH KD EXVFDGR D
YHFHVGHPDQHUDREVHVLYDFRPSXOVLYDWHQHUHOFRQWUROGHWRGR
ORTXHVXFHGH/RVDUWLVWDVTXHFRQRFHQODWHRUtDGHOFDRVVDEHQ
PX\ ELHQ TXH OD REVHVLyQ GH ´PDQWHQHU HO FRQWUROµ HV XQD
HQWHOHTXLD6DEHQTXHORVVLVWHPDVFDyWLFRVQRVRQSUHGHFLEOHV
PDQLSXODEOHV\FRQWURODEOHV\TXHHQOXJDUGHUHVLVWLUQRVDODV
LQFHUWLGXPEUHORTXHGHEHUtDPRVKDFHUHVDFHSWDUODV
&XDQGR DFHSWDPRV OD LQFHUWLGXPEUH FRPR XQD FDUDFWHUtVWLFD
SURFHVXDOFXDQGRDFHSWDPRVHOFDRVHVHQWRQFHVTXHDSDUHFH
ODFUHDWLYLGDG/DVLGHDVÁX\HQOLEUHPHQWHVLQQLQJ~QFRQWURO
SHUPLWLHQGR TXH OD FUHDWLYLGDG \ OD LPDJLQDFLyQ GLPDQHQ DVt
ODV LGHDV WLHQHQ VX WLHPSR SDUD QDFHU \ VX WLHPSR SDUD PRULU
(VRHVHOFDRVPXHUWH\QDFLPLHQWRGHVWUXFFLyQ\FUHDFLyQDO
PLVPRWLHPSR$FHSWDUODLQFHUWLGXPEUH\SHUPLWLUTXHÁX\DOD
LPDJLQDFLyQ QRV SHUPLWLUi DO PLVPR WLHPSR SRQHU DWHQFLyQ
D ODV SHTXHxDV VXWLOH]DV D ORV SHTXHxRV GHWDOOHV TXH SXHGHQ
SURYRFDUFDPELRVVLJQLÀFDWLYRVHQODFUHDFLyQGHODREUDHQORV
GLVWLQWRVHQIRTXHV\SRVLELOLGDGHV
<DHQOD*UHFLDFOiVLFDHQVXGLiORJRHQWUH$SRORQLXV\'DPLV
3KLORVWUDWRVKDEODEDGH´LPiJHQHVHQODVQXEHVµ\FRQFOXtDTXH
HUD FRQ OD D\XGD GH OD PHQWH GH REVHUYDGRU TXH VH IRUPDEDQ
WDOHVLPiJHQHVPLHQWUDVTXHHOSLQWRUGHEHXWLOL]DUDGHPiVVXV
PDQRVSDUDLPLWDUDODQDWXUDOH]D:8
3RU VX SDUWH 3OLQLR TXH GHVWDFDED HO SDSHO GHO D]DU HQ ODV
LQYHQFLRQHV GHO DUWH FXHQWD OD KLVWRULD GH XQ SLQWRU TXH VH
HVIRU]DED YDQDPHQWH HQ UHSUHVHQWDU OD HVSXPD HQ OD ERFD GH
XQSHUURKDVWDTXHGHVHVSHUDGRDUURMyXQDHVSRQMDHPSDSDGD
HQSLQWXUDDOSDQHO\SDUDVXVRUSUHVDHQFRQWUyHQODPDQFKD
GHMDGD SRU DTXHOOD HO HIHFWR TXH EXVFDED 6RQ ORV SULPHURV
HMHPSORVFRQRFLGRVHQORVTXHVHFLWDXQXVRSDUDODVDUWHVGH
HVWDV LPiJHQHV GH IRUPDFLyQ FRPSOHMD ´IUDFWDOµ SRGUtDPRV
GHFLU
!!"
3HURHV/HRQDUGRGD9LQFLHQVX!+:*:2&$2#$I91*(+:TXLHQQRV
GD XQD GHVFULSFLyQ PiV GHWDOODGD GHO SRGHU GH ODV ´IRUPDV
FRQIXVDVµFRPRODVGHODVQXEHVRHODJXDWXUELDSDUDHOHYDUHO
HVStULWXKDVWDQXHYDVLQYHQFLRQHV/OHJDLQFOXVRDGHVDFRQVHMDU
HQ DOJXQRV FDVRV HO WUDGLFLRQDO PpWRGR GHO GLEXMR PLQXFLRVR
SDUD UHFRPHQGDU HO HVER]R UiSLGR \ GHVRUGHQDGR TXH SXHGH
KDFHUVXUJLUQXHYDVSRVLELOLGDGHV
7HQGUtDLV TXH PLUDU FLHUWDV SDUHGHV PDQFKDGDV GH
KXPHGDGRSLHGUDVGHFRORUGHVLJXDO6LWHQpLVTXHLQYHQWDU
XQRVIRQGRVDOOtSRGUpLVYHUODLPDJHQGHSDLVDMHVGLYLQRV
DGRUQDGRVFRQPRQWDxDVUXLQDVURFDVERVTXHVJUDQGHV
OODQXUDVFROLQDV\YDOOHVHQJUDQYDULHGDG\OXHJRWDPELpQ
YHUpLV DOOt EDWDOODV \ H[WUDxDV ÀJXUDV HQ DFFLyQ YLROHQWD
H[SUHVLRQHV GH FDUDV \ URSDMHV \ XQD LQÀQLGDG GH FRVDV
TXHSRGUpLVUHGXFLUDVXVIRUPDVFRPSOHWDV\FRQGLJQDV
(QWDOHVSDUHGHVRFXUUHORVPLVPRTXHHQHOVRQLGRGHODV
FDPSDQDV HQ FX\R ULWPR HQFRQWUDUpLV FXDOTXLHU SDODEUD
DUWLFXODGDTXHSRGiLVLPDJLQDU::&
/RV WUDEDMRV GHO PHWHRUyORJR \ PDWHPiWLFR QRUWHDPHULFDQR
(GJDUG/RUHQ]HQODGpFDGDGHOGLHURQSDVRDORTXHKR\VH
FRQRFHFRPRHOHIHFWRPDULSRVDSRUORTXHVHOHFRQVLGHUDFRPR
XQRGHORVFUHDGRUHVGHODWHRUtDGHOFDRV/RUHQ]HPSOHDQGRXQ
PRGHORTXHFRPSUHQGtDWUHVYDULDEOHV³ODYHORFLGDGGHOYLHQWR
2%&)*'7+0-&4'2&%+*'&;&2%&.',)'*%.5*%J&+-.*145F1&'7.17&4%.17&'-&.*'7&
HFXDFLRQHVGLIHUHQFLDOHVRUGLQDULDVTXHOHSHUPLWLHUDQSUHGHFLU
HO WLHPSR DWPRVIpULFR /RUHQ] GHVFXEULy SRU FDVXDOLGDG TXH
VLWUDEDMDEDODVHFXDFLRQHVFRQYDORUHVLQLFLDOHVFRQGLIHUHQFLDV
PtQLPDVORVYDORUHVGHOPRGHORGLIHUtDQVLJQLÀFDWLYDPHQWHHQ
XQ WLHPSR UHODWLYDPHQWH FRUWR (O PRGHOR HUD PX\ VHQVLEOH D
ODVFRQGLFLRQHVLQLFLDOHVGLIHUHQFLDVGHPLOpVLPDVHQORVGDWRV
LQLFLDOHV SURYRFDEDQ HQRUPHV GLIHUHQFLDV HQ ORV UHVXOWDGRV
&RQGLFLRQHV LQLFLDOHV PX\ SDUHFLGDV SURGXFtDQ UHVXOWDGRV
WRWDOPHQWH GLIHUHQWHV HV GHFLU VL VH FRPHWHQ PLFURHUURUHV DO
ÀMDUODVFRQGLFLRQHVLQLFLDOHVpVWRVVHLQÁDUiQKDVWDFRQYHUWLUVH
HQPDFURHUURUHV(QORVVLVWHPDVOLQHDOHVQRVXFHGHORPLVPR
pVWRV FDPELDQ PX\ SRFR DO LQVHUWDU SHTXHxDV GLIHUHQFLDV
##$
SHTXHxRVHIHFWRVSURGXFHQSHTXHxRVFDPELRV(QODWHRUtDGHO
FDRV QR H[LVWHQ ORV VLVWHPDV OLQHDOHV VyOR ORV QR OLQHDOHV /DV
SUHGLFFLRQHV PHWHUHROyJLFDV GH DFXHUGR D HVWRV UHVXOWDGRV D
PHGLDQRRODUJRSOD]RQRHUDQSRVLEOHV(VWD
´GHSHQGHQFLD GH ODV FRQGLFLRQHV LQLFLDOHVµ VH H[SUHVD HQ OD
VLJXLHQWHIUDVH´3XHGHXQDPDULSRVDTXHDJLWDVXVDODVHQ%UDVLO
SURYRFDUXQWRUQDGRHQ7H[DVµ
(QWpUPLQRVJHQHUDOHVODWHRUtDGHOFDRVVRVWLHQHTXHODUHDOLGDG
HV XQ FRQWLQXXP GH RUGHQ GHVRUGHQ \ RUGHQ HWF \ WUDWD GH
HQWHQGHUTXpOH\HVULJHQHOSDVRGHXQDHWDSDDRWUD\TXHGHOFDRV
QDFHQQXHYDVHVWUXFWXUDVOODPDGDVHVWUXFWXUDV´GLVLSDWLYDVµ
8QVLVWHPDWLHQGHDHVWDUHQHVWDGRGHHTXLOLEULRVLQRH[LVWHXQ
HOHPHQWRSHUWXUEDGRUSHURVLHVWHHOHPHQWRH[LVWHHOVLVWHPD
SLHUGHHOHTXLOLEULR\FRPLHQ]DXQSURFHVRGHFDRVSURJUHVLYR
KDVWDDOFDQ]DUHOSXQWRGH´ELIXUFDFLyQµ(QHVWHSXQWRTXHHV
XQ HYHQWR R XQ DFRQWHFLPLHQWR TXH RFXUUH DO D]DU HO VLVWHPD
WLHQH GRV RSFLRQHV R ELHQ UHJUHVD DO HVWDGR GH HTXLOLEULR
RULJLQDO UHWURDOLPHQWDFLyQ QHJDWLYD R D WUDYpV GH XQ SURFHVR
GHUHWURDOLPHQWDFLyQSRVLWLYDFRPLHQ]DDDXWRRUJDQL]DUVHSDUD
HYROXFLRQDUHQXQDQXHYDHVWUXFWXUDODHVWUXFWXUD´GLVLSDWLYDµ
R´GLVSHUVLYDµ(VWHWLSRGHHVWUXFWXUDHVGHQRPLQDGDGLVLSDWLYD
GHELGRDTXHFRQVXPHPXFKRPiVHQHUJtDTXHODVHVWUXFWXUDV
RULJLQDOHV9HPRVSXHVTXHGHOFDRVWDPELpQSXHGHQDFHUHO
RUGHQ
Dos conceptos más sobre la teoría del caos: el
atractor de Lorenz y la geometría fractal
(O WpUPLQR IUDFWDO IXH LQWURGXFLGR UHFLHQWHPHQWH SRU %HQRLW
0DQGHOEURW 6RQ PX\ FRPXQHV HQWUH ORV PDWHPiWLFRV GRV
HMHPSORVODFXUYDGH.RFK\HOFRQMXQWRGH&DQWRU$PERVVRQ
VLPLODUHVDVtPLVPRV\FRQVWLWX\HQPHFDQLVPRVFRPXQHVSDUD
FRQVWUXLUIUDFWDOHV3RUVXSXHVWRH[LVWHQRWURVLQVWUXPHQWRVTXH
LQWHJUDQHO]RRGHPRQVWUXRVIUDFWDOHVLQFOX\HQGRHOFRQMXQWR
!!"
GH0DQGHOEURWTXHVRQPX\~WLOHVSDUDGHVFULELUORVIHQyPHQRV
GHODQDWXUDOH]D3HUR¢TXpHVXQIUDFWDO"(QWpUPLQRVVHQFLOORV
XQ IUDFWDO HV XQD ÀJXUD TXH HVWi FRPSXHVWD SRU SHTXHxDV
SDUWHV ODV FXDOHV VRQ LJXDOHV D OD ÀJXUD RULJLQDO /RV IUDFWDOHV
WLHQHQVLPLOLWXGSURSLD/DQDWXUDOH]DVHH[SUHVDDWUDYpVGHVX
SURSLDJHRPHWUtDORVIUDFWDOHV/DHVHQFLDGHORVIUDFWDOHVHVOD
´UHWURDOLPHQWDFLyQµ (O SXQWR GH SDUWLGD HV XQD LQIRUPDFLyQ
RULJLQDO SURFHVDUOD \ REWHQHU XQ UHVXOWDGR (VWH VH SURFHVD
GH QXHYR \ VH REWLHQH RWUR UHVXOWDGR \ VH FRQWLQ~D KDFLHQGR
OR PLVPR LQGHÀQLGDPHQWH FRQ FDGD UHVXOWDGR KDVWD WHQHU XQ
UHVXOWDGR H[WUDxR (VWH UHVXOWDGR IRUPD XQD ÀJXUD H[WUDxD
OODPDGRDWUDFWRU\pVWHSRVHHSURSLHGDGHVIUDFWDOHV(ODWUDFWRU
PLVPRHVXQIUDFWDO
/D HUD GH OD UHSURGXFWLYLGDG HQ OD TXH QRV HQFRQWUDPRV HV
SRVLEOHGHPRVWUDUXQDPXOWLWXGGHGHULYDFLRQHVVREUHXQPLVPR
FRQFHSWR R SXQWR GH LQLFLR FUHDWLYR GDQGR XQD YDULHGDG GH
UHVXOWDGRVHQORVTXHHOQ~PHURGHHOORVORVGHWHUPLQDHOSURSLR
DUWLVWD5HFRUGHPRVGHVGHODVVHULHVGHREUDVUHSHWLGDVKDVWDORV
WUDEDMRVFRQORVQXHYRVPHGLRVFRPRLQVWDODFLRQHVLQWHUDFWLYDV
QHWDUW \ PiV HQ DTXHOORV PXOWLGLVFLSOLQDUHV HQ ORV TXH OD UH
SURGXFFLyQVHUHDOL]DHQYDULRVFDQDOHV(LQVWHLQSRUHMHPSOR
DÀUPyTXH
(OWLHPSRHOHVSDFLR\ODPDWHULDQRVRQFRQGLFLRQHVHQ
ODVTXHYLYLPRVVLQRHVTXHPDVPHQWDOHVFRQDUUHJORDORV
FXDOHVSHQVDPRV
/D PHQWH KXPDQD WUDEDMD VREUH ORV GDWRV TXH UHFLEH FRPR HO
HVFXOWRU VREUH VX EORTXH GH PiUPRO 'LIHUHQWHV HVFXOWRUHV
SXHGHQH[WUDHUHVWDWXDVGLIHUHQWHVGHOPLVPREORTXH/DPHQWH
DO FDSWDU OD UHDOLGDG HV VHOHFWLYD /RV LQGLYLGXRV GHÀQHQ XQ
1*4'-&'-&217&'2','-.17&4'&757&)'*/')/+1-'7&'-&B5-/+0-&4'&757&
LQWHUHVHV YDORUHV H[SHULHQFLDV VLVWHPD SVtTXLFR HWF ([LVWHQ
PXFKDVLQWHUSUHWDFLRQHVGHXQDPLVPDUHDOLGDG\SRUORWDQWR
PXFKDV YLVLRQHV GHO XQLYHUVR %DMR OD SHUVSHFWLYD KRORJUiÀFD
QXHVWURVFHUHEURVFRQVWUX\HQPDWHPiWLFDPHQWHODUHDOLGDGGHVGH
XQDGLPHQVLyQTXHWUDVFLHQGHHOWLHPSR\HOHVSDFLRDWUDYpVGH
##$
OD LQWHUSUHWDFLyQ GH ODV IUHFXHQFLDV GH ORV GDWRV TXH SHUFLEHQ
GH ORV REMHWRV R IHQyPHQRV GHO PXQGR /DV LQYHVWLJDFLRQHV
VREUHORVKRORJUDPDVFRQWLQ~DQ(VSRVLEOHTXHDOJ~QGtDSXHGD
FRPSUREDUVH TXH OR TXH YHPRV VRQ KRORJUDPDV \ TXH SRU
OR WDQWR QRVRWURV PLVPRV VRPRV LPiJHQHV KRORJUiÀFDV pVWR
VLJQLÀFD TXH FDGD XQR GH QRVRWURV VLHQGR SDUWH GH HVD JUDQ
XQLGDG SRVHHPRV WRGD OD LQIRUPDFLyQ VREUH HO SUHVHQWH HO
SDVDGR\HOIXWXURGHORVHUHVKXPDQRV\GHOXQLYHUVR'HDTXt
TXH WRGDV QXHVWUDV DFFLRQHV DIHFWDQ D ORV GHPiV (Q UHDOLGDG
OD FLHQFLD DGPLWH OD SRVLELOLGDG GH TXH XQD DFFLyQ D GLVWDQFLD
LQÁX\D VLPXOWiQHDPHQWH HQ WRGRV OR SXQWRV GHO HVSDFLR VLQ
QHFHVLGDGGHTXHH[LVWDQLQJXQDIXHU]DYLVLEOHTXHYLDMHDWUDYpV
GHO HVSDFLR PLVPR (VWR HV OR TXH HQ ItVLFD VH FRQRFH FRPR
´HQWUHOD]DPLHQWR FXiQWLFRµ 7RGR VH FRQHFWD FRQ WRGR XQD
SDUWHGHODUHDOLGDGRXQDVXEWRWDOLGDGFRPRODOODPDED%RPK
WLHQHODLQIRUPDFLyQGHOWRGR
0DWHPiWLFRV\DUWLVWDVQHFHVLWDQSURJUHVDUHQODUHSUHVHQWDFLyQ
GH VLWXDFLRQHV PiV FRPSOHMDV TXH RFXUUHQ HQ OD UHDOLGDG (O
HVWXGLRGHHVSDFLRVGHIDVHVTXHUHSUHVHQWDQWRGDVODVSRVLEOHV
SRVLFLRQHVKDD\XGDGRDFRPSUHQGHUPHMRUHOSODQRSUR\HFWLYR
8QDEXHQDYLVXDOL]DFLyQGHHMHPSORVVHQFLOORVSXHGHVHUXVDGD
GHVSXpV HQ HMHPSORV PiV FRPSOLFDGRV (V SUHFLVR PpWRGRV
JHQHUDOHV
(V XQ KHFKR GHPRVWUDGR TXH ORV OtPLWHV HQ OD SURGXFFLyQ
DUWtVWLFD\VREUHWRGRHQODUHVROXFLyQGHSURSXHVWDVFUHDQXQ
SUREOHPDGHELGRDTXHHOVRSRUWHRHOPHGLRQRLGHQWLÀFDQSRU
VL VRORV UHDOPHQWH DO DUWLVWD VLQR VX WUD\HFWRULD SURGXFWLYD HQ
EDVHDVXVLGHDV\ODSHUVSHFWLYDFRQODTXHDIURQWDHOPXQGRHQ
HOTXHYLYHHLQWHUYLHQH
/DWUDQVGLVFLSOLQDULHGDGHQHODUWLVWDFRPHQWDGDDQWHULRUPHQWH
HV XQD UHDOLGDG SUREOHPiWLFD SDUD HO VLVWHPD /RV OtPLWHV VH
FRQIXQGHQ\GLÀHUHQHQWUHHOORV3RUTXHDOLJXDOTXHHQHOPRGR
FDUWHVLDQRHOSODQRHV~QLFRHQVXUHDOLGDG\OLQHDO(QHODUWH
HO VRSRUWH \ OD WpFQLFD HVWDED GHÀQLGD SRU SDWURQHV VLPLODUHV
GLEXMRSLQWXUDHVFXOWXUDHWF
!!"
/DSURSXHVWDVREUH´GLEXMRFRPSXHVWRµHVHQHVHQFLDODHYLGHQFLD
GHTXHODVLPXOWDQHLGDG\HOGHVGREODPLHQWRGHOSODQRFDUWHVLDQR
QRVPXHVWUDQXHYDVUHDOLGDGHV(QXQSULPHUWpUPLQRHOGLEXMR
FRPSXHVWR TXH VH HVSHFLÀFD HQ HO DSDUWDGR VLJXLHQWH FRQVLVWH
HQHOSURFHVRGHGLEXMDUTXHHVHQVtPLVPRREUDDUWtVWLFDVX
QDUUDWLYDVHFRPSRUWDFRPRSLH]D
El dibujo compuesto
/RVQXHYRVFRPSRUWDPLHQWRVDUWtVWLFRVJHQHUDGRVDWUDYpVGHODV
QXHYDVWHFQRORJtDVGHODLPDJHQLQWURGXMHURQQXHYRVPRGHORVGH
SHQVDPLHQWR\IRUPDVGHSHUFHSFLyQJHQHUDQGRDVtFDPELRV\
WUDQVIRUPDFLRQHVHQODVREUDVHQORVPRGRVGHSURGXFLUODV\GH
UHSUHVHQWDUODV/DVUHVWULFFLRQHVGHHVWH´VLVWHPDµYDQDUHJXODU
GH GLIHUHQWHV PDQHUDV OD UHODFLyQ HQWUH HO DUWLVWD OD REUD \ HO
HVSHFWDGRU(VWHHVWXGLRVHRUJDQL]DVREUHORVPRGRVHQTXHVH
FRQVWLWX\H\SUHYpODÀJXUDKLSRWpWLFDGHOHVSHFWDGRUDSDUWLUGH
217&%7)'/.17&/1-/'*-+'-.'7&%&2%&+,%3'-&;&757&*'7.*+//+1-'7&/1,1&
HVHOYLGHR,PSRVLEOHHV\DWHQHUXQSXQWRGHYLVWDÀMR´HQXQ
PXQGRGRQGHWRGRDFRQWHFHVLPXOWiQHDPHQWHµ
(OSURFHVREiVLFRIUDFWDULRHQHOTXHVHRULJLQDXQDSLH]DJUiÀFD
'7&+-.'*'7%-.'&'-&/5%-.1&7'&)*'7'-.%&5-%&7'/5'-/+%&2+-'%2&'-&'2&
WLHPSRTXHYDGHVFULELpQGRVHPHGLDQWHWUD]RVHQXQSODQRWLSR
R PXHVWUD (O HQIRTXH \ SXQWR GH YLVWD WUDGLFLRQDO VH URPSH
FXDQGR HO SODQR PXHVWUD GHMD GH VHU YLQFXODQWH FRPR IRQGR
HQ OD OHFWXUD GH OD REUD 3RU FRQVLJXLHQWH OD OtQHD UHFXSHUD VX
SURWDJRQLVPRGLQiPLFRVHOLEHUDGHOVRSRUWHHQFLHUWDPHGLGD
(O DVSHFWR WHyULFR GH OD SURSXHVWD GH GLEXMR FRPSXHVWR VH
UHÀHUHDREMHWLYRVVREUHODKLSyWHVLVGHTXHHOSDUWLFLSDQWHSXHGH
FRQÀJXUDU FRPSOHWDU \ GHFLGLU GH XQD IRUPD FRQVFLHQWH \R
LQFRQVFLHQWH VX SURSLR UHFRUULGR YLVXDO \ H[SHULHQFLDO GH ORV
GLEXMRV (Q HO SURFHVR ODV YDULDEOHV GH SRVLFLyQ PRYLPLHQWR
\ YHORFLGDG GHO XVXDULR KDFLD OD SLH]D \ D OD LQYHUVD VRQ
4'.'*,+-%-.'7&)%*%&/1,)2'.%*&2%&2'/.5*%&4'&2%&,+7,%&4'&,%-'*%&
##$
LQGLYLGXDOHQJOREDGDHQXQDUHODFLyQHVSDFLRWHPSRUDO~QLFDH
LUUHSHWLEOH
/RVPHFDQLVPRVGHWUDEDMRDWHQFLyQ\SURFHVRWUDGLFLRQDOHQHO
DFWRGHGLEXMDURLQFOXVRHOSURSLRSURFHVRFUHDWLYRGHHVFULELU
SLQWDUHWFVXHOHVHUSULPHURLPDJLQDUSDUDGHVSXpVWUDVODGDU
VXSUR\HFFLyQGHVGHODPDQRFRQXQDKHUUDPLHQWDDXQVRSRUWH
(O HQIRTXH TXH VH SHUVLJXH HV VLQ OXJDU D GXGDV GHVGREODU HO
VRSRUWH HQ HO TXH VH HVFULEH R GLEXMD GLIHUHQFLDU QLYHOHV HQ
ORV TXH HO UDVJR R WUD]R SXHGH VDOWDU GH SODQR (O SODQR GHMD
GH VHU OLWHUDOPHQWH SODQR SDUD SDVDU D IXQFLRQDU FRPR QLYHOHV
GH IXQFLRQDOLGDG FUHDWLYD HQ ORV FXDOHV HO LQWHUpV QR HV \D ORV
SODQRV HQ Vt VLQR HO WUDQVLWR HQWUH XQ QLYHO \ RWUR (O VHQWLGR
GHYHUWLFDOLGDGHQWUHQLYHOHV/DOHFWXUDSXHGHVHUOLQHDOHQXQ
PLVPRQLYHORPXOWLOLQHDOHQYDULRVQLYHOHV
/DGHÀQLFLyQGH´GLEXMRFRPSXHVWRµVHHVWDEOHFHHQIXQFLyQGH
XQDVFDUDFWHUtVWLFDVTXHOHVRQSURSLDVFRPRVRQ
‡ (O SURFHVR FRQVWUXFWLYR HQ OD OtQHD GH WLHPSR KDVWD VX
FRQFOXVLyQHVHQVtHOIRUPDWRGHÀQLWLYRGHODREUDJUiÀFD
‡ (O GLEXMR QDFH GHVGH FXDOTXLHU SODQR KRPRJpQHR GHO
HVSDFLR\VHGHVDUUROODHQHOWLHPSRSUR\HFWiQGRVH
‡ /D LPSRUWDQFLD UDGLFD HQ HO UHVXOWDGR SURFHVXDO GRQGH
ODVFRPSRVLFLRQHVGHWUD]RVDYDQ]DQFRQVWUX\HQGRHOWHPD
SURSXHVWRSRUHODUWLVWD
‡8QDYH]FRQFOXLGDODSLH]DSXHGHUHSURGXFLUVHHQHOWLHPSR
SURSLR\HVDXWyQRPDQRSUHFLVDGHPHFDQLVPRVVRÀVWLFDGRV
SDUDGHVHQYROYHUVH
‡ (O SURFHVR GH OHFWXUD HV HO KDELWXDO GH FXDOTXLHU SLH]D
QDUUDWLYDOLWHUDULDFLQHPDWRJUiÀFDHWF
‡ /DV GHFLVLRQHV TXH UHDOL]D HO DUWLVWD HQ FDGD LQVWDQWH VRQ
GHWHUPLQDQWHV SDUD OD FRPSRVLFLyQ JUDÀFD VLJXLHQWH /RV
HUURUHV \ DFLHUWRV VH YLVXDOL]DQ SRU OR TXH HO FRQWHQLGR
GLGiFWLFRHVWiLPSOtFLWR
!!"
‡ (O PRPHQWR FUHDWLYR HV FRPSOHWR SRUTXH VH GHVYHOD OD
DFFLyQQDUUDGDOLWHUDOPHQWHSRUHODUWLVWDHQHOVRSRUWH
‡ (O FDPELR GH SDUiPHWURV FRPR HO VRSRUWH TXH D PRGR
GH IRWRJUDPD YD JXDUGDQGR ORV SDVRV GHO SURFHVR GH
FRQVWUXFFLyQGHODSLH]D/DFDUDFWHUtVWLFDIXQGDPHQWDOUDGLFD
HQ HO UHYHODGR GH FDGD XQD GH ODV IDVHV TXH VH HVWDEOHFHQ
SUHYLDPHQWHFRPRSRUHMHPSORFRQVWUXFFLyQFRPSRVLFLyQ
HWF
(OGLEXMRVHFRQIRUPDUtDHQHOUHFRUULGRGHOWUD]RHQXQVRSRUWH
SODQRTXHVHGHVGREODDPRGRGHFDSDV
/DV SRVLELOLGDGHV GH OD DFWLYLGDG FUHDWLYD YDUtDQ DVt FRPR VXV
UHVXOWDGRVVLWRPDPRVFRPRUHIHUHQFLDD
/DV SUR\HFFLRQHV TXH UHVXOWDQ GH ORV WUD]RV HQ XQ SODQR
SHUSHQGLFXODURKRUL]RQWDO
/DUHVXOWDQWHGHFRPELQDUYDULRVSODQRVHQORVTXHORVWUD]RV
'-& 4'.'*,+-%417& )5-.17& 7%2.%-& 4'& 5-1& %& 1.*1& '-& B5-/+0-& %&
FULWHULRVHVWDEOHFLGRV
/DVSUR\HFFLRQHVGLVWRUVLRQDGDVRFXUYDGDVGHORVWUD]RVHQ
HOPRPHQWRGHVDOWDUGHSODQRRQLYHO
6L FRQVLGHUDPRV HO WLHPSR FRPR SURFHVR GH FRQVWUXFFLyQ
PXOWLOLQHDO \ VX OHFWXUD YLVXDO SRU XQ LQGLYLGXR WLSR HVWH
FRQVWUXLUtDVXH[SHULHQFLDOLQHDO
Fig. 3. Imagen en capas.
##$
$FHUFDGHOVRODSDPLHQWR\VLPXOWDQHLGDGHQORVQXHYRVPHGLRV
0DUWtQ3UDGDDxDGH
/DV IRUPDV GH YLVLyQ SURSLDV GH ORV QXHYRV PHGLRV
FRQVLVWHQHQXQDQRSHUVSHFWLYDHQXQQRPLUDUDWUDYpV
9LVLyQ GHO VRODSDPLHQWR GHO WUDVODSDPLHQWR SHUFHSWXDO
FDUDFWHUtVWLFR GH ORV VLVWHPDV RSHUDWLYRV \ SURJUDPDV
EDVDGRV HQ YHQWDQDV TXH VH DEUHQ \ VH VRODSDQ \ TXH
FRQIRUPDQVLVWHPDVGHRSDFLGDGSDUFLDO«(OSURFHVR
GH HODERUDFLyQ GH OD LPDJHQ GLJLWDO HV XQD FRPSOHMD
DFXPXODFLyQ\VHGLPHQWDFLyQGHLPiJHQHVTXHVHVRODSDQ
VLQGHVDSDULFLyQ(VWUDWLJUDItDDFRJLGDSHUPDQHQWHPHQWHDO
)*+-/+)+1&4'&7+,52.%-'+4%4&)*1)+%&4'&75&'7.*5/.5*%&.6/-+/%&
\SURFHVXDOTXHODVLQLFLDWLYDVDUWtVWLFDVPiVUDGLFDOHVGH
DQiOLVLVGHOVRIWZDUH\GHODVWHRUtDVGHOLQWHUID]WUDWDQGH
YLROHQWDU FUHDQGR HFRV HQWUH ODV FDSDV XQD WHFWyQLFD GH
WUDVODSDPLHQWRV\VXSHUÀFLHV
'HDTXtTXHODVSURSXHVWDVDUWtVWLFDVVXUJLGDVHQHOPHGLR
VH HVWUXFWXUHQ HQ WRUQR D HVWD VLPXOWDQHLGDG WDPELpQ GH
tQGROH HVSDFLDO \ H[SHULPHQWDO 'H KHFKR ODV FUHDFLRQHV
DUWtVWLFDV GLJLWDOHV GHPXHVWUDQ FyPR HQ HOODV HV SRVLEOH
5-& ,%;1*& %/'*/%,+'-.1& '-.*'& 2%7& 417& 4+,'-7+1-'7&
.*%4+/+1-%2,'-.'& /1-7+4'*%4%7& /1,1& )*1)+%7& 4'& .14%&
REUD GH DUWH OD GLPHQVLyQ VHJ~Q OD FXDO VH H[WLHQGHQ
VLPXOWiQHDPHQWH HO WRWDO GH ORV HVWUDWRV \ OD RWUD SRU OD
TXHODVSDUWHVVHVXFHGHQXQDVDRWUDV:<&
(OWLHPSRPDUFDODGLUHFFLyQGHXQDUHFWDHQHOHVSDFLR3HUR
HO SODQR P~OWLSOH HV XQ GHVGREODPLHQWR GHO HXFOLGLDQR SRU
OD SUHVHQFLD GHO WLHPSR \ VX UHODWLYLGDG YD UHODFLRQDGD FRQ OD
FXUYDWXUD GH DPERV TXH VLHPSUH HV SDUDOHODPHQWH FDyWLFD
R IUDFWDULD (O IUDFWDO WLHQH XQ SXQWR GH LQWHUVHFFLyQ R SXQWR
GRQGHODFXUYDWXUDRGHVGREODPLHQWRVHRULJLQDÀQDOL]DHQXQ
HVSDFLRWLHPSRSURSLR
(Q HVWD HWDSD DFWXDO GHO DUWH HQ UHYROXFLyQ TXH HYROXFLRQD
UiSLGDPHQWHVHDEUHQQXHYDVSRVLELOLGDGHV\GHXQDIRUPDPiV
!!"
SUHFLVDVHYLQFXODODLQWHUDFFLyQGHODLQIRUPDFLyQORFDOL]DFLRQHV
\XQDVRFLHGDGHQFRQWLQXRPRYLPLHQWR6XUJHQSRVLELOLGDGHVHQ
ODVTXHHOHVSDFLR\ODVDOWHUQDWLYDVGHPHGLFLyQ\ORFDOL]DFLyQVH
WUDQVIRUPDQHQOyJLFDVDMHQDVDODIRUPD\TXHVRQPiVSURSLDV
GHRWUDVGLVFLSOLQDV\VLQHPEDUJRFRQHOFRPSXWDGRUVHSXHGHQ
LQFRUSRUDUDODOyJLFDGHOHVSDFLR\GHODFRQVWUXFFLyQ
)UHQWH D RWURV GLVSRVLWLYRV GH SURGXFFLyQ DUWtVWLFD DFWXDOHV HO
FRUUHVSRQGLHQWH DO GLEXMR FRPSXHVWR FRPR UHVXOWDGR JUiÀFR
KDELOLWD \ JHQHUD QXHYDV YtDV GH DSURSLDFLyQ GHO PHQVDMH
HVWpWLFRSRUHOORHVSRVLEOHDGYHUWLUHQWRQFHVHOXVRGHSUiFWLFDV
LQKHUHQWHV D OD SURGXFFLyQ DUWtVWLFD \ TXH SRQHQ HQ MXHJR DO
VLVWHPDGHUHODFLRQHVFRPSUHQGLGRHQWUHHOGLVSRVLWLYRHODUWLVWD
\HOHVSHFWDGRU
##$
D1.%7
8
(OFDUiFWHUÀJXUDWLYRRQRÀJXUDWLYRVHUHÀHUHDODUHODFLyQPiVRPHQRVGLUHFWDFRQORV
REMHWRVUHDOHVFRQORVTXHVHUHODFLRQ
$
/RVSRVWXODGRVGH(XFOLGHVTXHUHFRJHHQVXOLEURGH)&,$;)#C#1*&,&'7/*+.1&%2*'4'41*&4'&
ORVDxRV$&VRQ&
'DGRVGRVSXQWRVVHSXHGHQWUD]DUXQDUHFWDTXHORVXQH&
&XDOTXLHUVHJPHQWRSXHGHVHUSURORQJDGRGHIRUPDFRQWLQXDHQXQDUHFWDLOLPLWDGD
HQODPLVPDGLUHFFLyQ&
6HSXHGHWUD]DUXQDFLUFXQIHUHQFLDGHFHQWURHQFXDOTXLHUSXQWR\UDGLRFXDOTXLHUD&
7RGRVORViQJXORVUHFWRVVRQLJXDOHV&
6LXQDUHFWDDOFRUWDUDRWUDVGRVIRUPDORViQJXORVLQWHUQRVGHXQPLVPRODGR
PHQRUHVTXHGRVUHFWRVHVDVGRVUHFWDVSURORQJDGDVLQGHÀQLGDPHQWHVHFRUWDQGHO
ODGRHQHOTXHHVWiQORViQJXORVPHQRUHVTXHGRVUHFWRV(VWH~OWLPRSRVWXODGRTXH
HVFRQRFLGRFRPRHOSRVWXODGRGHODVSDUDOHODVIXHUHIRUPXODGRFRPR´3RUXQSXQWR
H[WHULRUDXQDUHFWDVHSXHGHWUD]DUXQD~QLFDSDUDOHODµ
3LQR3DROR<9:)&A&$29$I9**(+:9HQHFLD*KHUDUGRHGFUtWLFDLQWURGXFFLyQ\
QRWDVGH5RGROIR\$QQD3DOOXFFKLQL9HQHFLD*XDUQDWLHG&UtWLFDGH6XVDQD
)DODEHOOD5RPD/LWKRV
<
6iQFKH] -RVp $ I+F0*90:$ :+*=,*90:$ 5$ 8&)=*90:,$ 0()*(+:)#, DOJXQDV SURSXHVWDV GHVGH OD
XQLYHUVLGDG FRRUG SRU -RVp $QWRQLR *yPH] +HUQiQGH] -RVp $QWRQLR 6iQFKH]
0DUWtQH] ´QXHYRV HVSDFLRV SDUD HO DUWHµ 8QLYHUVLGDG GH 0XUFLD $XOD GHEDWH ,6%1SS
=
! 6HIFKRYLFK * :DLVEXUG * +DFLD XQD 3HGDJRJtD GH OD &UHDWLYLGDG ([SUHVLyQ SOiVWLFD
7ULOODV0p[LFR')S
!%X]DQ7RQ\;)$)9?+&$2#$)&,$C:8:,$C#1*:)#,HGLFLyQHQHVSDxRO8UDQR%DUFHORQD
SS
>
! 6iQFKH] 'RPtQJXH] 0DULR ´/D LPDJLQDFLyQ \ HO SUREOHPD LPDJLQDULRµ 5HYLVWD
DBC:2:,Qž8QLYHUVLGDG&RPSOXWHQVHGH0DGULG
!!"
?
9pDVH *RPEULFK (UQVW + .+*#$ #$ 9)(,9B1S$ ;,*(29&$ ,&?+#$ ):$ 8,90&)&A=:$ 2#$ ):$ +#8+#,#1*:09B1$
890*B+90:(GLWRULDO*XVWDYR*LOL%DUFHORQDS
#
!$UQKHLP5XGROI'&1,92#+:09&1#,$,&?+#$):$#2(0:09B1$:+*=,*90:3DLGyV%DUFHORQDS
89
!%RXUULDXG1;,*"#*9G(#$+#):*9&11#))#3DUtV/HV3UHVVHVGXUpHOS
88
3HUDQ0.+G(9*#0*(+:,$8:+:$#)$:0&1*#09C9#1*&>&DWiORJR@(VSDLG·DUWFRQWHPSRUDQL
GH&DVWHOOyQMXOLRVHSWLHPEUH
8:
!&DEH]DV/LQR´0iTXLQDVGHGLEXMDUµHQ0iTXLQDV\KHUUDPLHQWDVGHGLEXMR(G
&iWHGUD0DGULGS
8<
/DQGDX/\5XPHU<¢4XpHVODWHRUtDGHODUHODWLYLGDG"$NDO0DGULG"!
&&KRSUD'HHSDN&XHUSRVVLQHGDGPHQWHVVLQWLHPSR(G9HUJDUDS
&
8=
!9pDVHHQOtQHDKWWSZZZSK\VRUJFRPQHZVKWPOVHS
! 0DUWtQ 3UDGD -/ ´/DV LQVWUXFFLRQHV GHO VRIWZDUH \ GHO KDUGZDUH FRPR QXHYRV
PDQXDOHVGHGLEXMRµHQ0iTXLQDV\KHUUDPLHQWDVGHGLEXMR(G&iWHGUDSS
0DGULG
8>
!9pDVHHQOtQHDGH/XFDV/LQDUHV-DYLHUKWWSSODWHDSQWLFPHFHVaMGHOXFDVMGHOXFDV
KWP&
8?
! .DUO 3ULEUDQ QHXUyORJR \ QHXURFLUXMDQR SRVWXOD OR VLJXLHQWH ´1XHVWUR FHUHEUR
FRQVWUX\H PDWHPiWLFDPHQWH OD UHDOLGDG LQWHUSUHWDQGR IUHFXHQFLDV TXH YLHQHQ GH RWUD
GLPHQVLyQGRPLQLRGHUHDOLGDGVLJQLÀFDQWHSULPDULDPHQWHDUTXHWtSLFDTXHWUDQVFLHQGH
HOWLHPSR\HOHVSDFLR(OFHUHEURHVXQKRORJUDPDLQWHUSUHWDQGRXQXQLYHUVRKRORJUiÀFRµ
8#
!%RKP'DYLG3:$!&*:)92:2$5$#)$>+2#1$MC8)90:2&(G&DLURV
:9
!7LSOHU)UDQN-3:$6=,90:$2#$):$91C&+*:)92:G$OLDQ]D8QLYHUVLGDG0DGULGS
!*RPEULFK(UQVW+.+*#$#$9)(,9B1S$;,*(29&$,&?+#$):$8,90&)&A=:$2#$):$+#8+#,#1*:09B1$890*B+90:
(GLWRULDO*XVWDYR*LOL%DUFHORQD
:8
##$
::
!9LQFL/HRQDUGRGD$'(:2#+1&$2#$1&*:,(GLFLRQHV)HOPDU0DGULG!
!0DUVKDOO0F/XKDQ&RQIHUHQFLDSURQXQFLDGDHQ)ORULGD6WDWH8QLYHUVLW\!
:<
! 0DUWtQ 3UDGD -/ ´/DV LQVWUXFFLRQHV GHO VRIWZDUH \ GHO KDUGZDUH FRPR QXHYRV
PDQXDOHVGHGLEXMRµHQ0iTXLQDV\KHUUDPLHQWDVGHGLEXMR(G&iWHGUD3DJ
0DGULG
!!"
BIBLIOGRAFIA
$51+(,05XGROI'&1,92#+:09&1#,$,&?+#$):$#2(0:09B1$:+*=,*90:3DLGyV
%DUFHORQDS
%5($-RVp/XLV/DHUDSRVWPHGLD$FFLyQFRPXQLFDWLYDSUiFWLFDVSRVW
DUWtVWLFDV\GLVSRVLWLYRVQHRPHGLDOHV(GLWDGRHQIRUPDWR3')HORFWX
EUH
%2855,$8'1;,*"#*9G(#$+#):*9&11#))#3DUtV/HV3UHVVHVGXUpHO
%8=$17RQ\;)$)9?+&$2#$)&,$C:8:,$C#1*:)#,HGLFLyQHQHVSDxRO
8UDQR%DUFHORQD
&+235$'HHSDN&XHUSRVVLQHGDGPHQWHVVLQWLHPSR(G9HUJDUD
(,61(5(OOLRW:(GXFDUODYLVLyQDUWtVWLFD(G3DLGyV%DUFH
ORQD
*20%5,&+(UQVW+.+*#$#$9)(,9B1S$;,*(29&$,&?+#$):$8,90&)&A=:$2#$):$
+#8+#,#1*:09B1$890*B+90:(GLWRULDO*XVWDYR*LOL%DUFHORQD
*Ð0(=0ROLQD-XDQ-RVpFRRUG0iTXLQDV\KHUUDPLHQWDVGHGLEXMR
(GLWRULDO&iWHGUD(GLFLyQ0DGULG
+$:.,1*6WHSKHQ:+LVWRULDGHOWLHPSR'HOELJEDQJDORVDJXMHURV
1#A+&,(GLWRULDO&UtWLFD%DUFHORQD
+$:.,1*6WHSKHQ:(OXQLYHUVRHQXQDFiVFDUDGHQXH](GLWRULDO
&UtWLFD%DUFHORQD
+$:.,1*6WHSKHQ:3HQURVH5RJHU/DQDWXUDOH]DGHOHVSDFLR\
#)$*9#C8&(GLWRULDO'HEDWH0DGULG
/$1'$8/\5XPHU<¢4XpHVODWHRUtDGHODUHODWLYLGDG"$NDO0D
GULG
##$
02/,1$$QJHOD\/DQGD.HSD)XWXURVHPHUJHQWHVDUWHLQWHUDFWLYLGDG\
QXHYRV9DOHQFLD,QVWLWXFLy$OIRQVHO0DJQiQLP
3(5$10$.+G(9*#0*(+:,$8:+:$#)$:0&1*#09C9#1*&>&DWiORJR@(VSDLG·DUW
FRQWHPSRUDQLGH&DVWHOOyQMXOLRVHSWLHPEUH
3,123DROR<9:)&A&$29$I9**(+:9HQHFLD*KHUDUGRHGFUtWLFD
LQWURGXFFLyQ\QRWDVGH5RGROIR\$QQD3DOOXFFKLQL9HQHFLD*XDU
QDWLHG&UtWLFDGH6XVDQD)DODEHOOD5RPD/LWKRV
3(1526(5RJHU;)$0:C91&$:$):$+#:)92:2-$71:$A(=:$0&C8)#*:$2#$):,$)#5#,$
GHOXQLYHUVR(G'HEDWH
6É1&+(=-RVp$I+F0*90:$:+*=,*90:$5$8&)=*90:,$0()*(+:)#,-$:)A(1:,$8+&8(
HVWDVGHVGHODXQLYHUVLGDGFRRUGSRU-RVp$QWRQLR*yPH]+HUQiQGH]
-RVp$QWRQLR6iQFKH]0DUWtQH]´QXHYRVHVSDFLRVSDUDHODUWHµ8QL
YHUVLGDGGH0XUFLD$XODGHEDWH
6É1&+(='RPtQJXH]0DULR´/DLPDJLQDFLyQ\HOSUREOHPDLPD
JLQDULRµ5HYLVWDDBC:2:,Qž8QLYHUVLGDG&RPSOXWHQVHGH0DGULG
6()&+29,&+*:DLVEXUG*+DFLDXQD3HGDJRJtDGHOD&UHDWLYLGDG
;O8+#,9B1$8)F,*90:7ULOODV0p[LFR')
6&+5g',1*(5(GZLQ/DHVWUXFWXUDGHOHVSDFLRWLHPSR$OLDQ]D8QL
YHUVLGDG0DGULG
7,3/(5)UDQN-3:$6=,90:$2#$):$91C&+*:)92:2$OLDQ]D8QLYHUVLGDG
0DGULG
9,1&,/HRQDUGRGD'(:2#+1&$2#$1&*:,(GLFLRQHV)HOPDU0DGULG
!!"
##$
Descargar