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==由分形而诞生的创造性作品==

==由分形而诞生的创造性作品==

自1999年以来，超过10个科学团队对'''杰克逊 · 波洛克 Jackson Pollock''''(1912-1956)的50多幅油画进行了分形分析，这些油画是直接将颜料倒在水平画布上创作出来的。<ref>{{cite journal |first=R. P. |last=Taylor |display-authors=etal |title=Fractal Analysis of Pollock's Drip Paintings |journal=Nature |volume=399 |issue=6735 |page=422 |year=1999|bibcode=1999Natur.399..422T |doi=10.1038/20833 }}</ref><ref>{{cite journal |first1=J. R. |last1=Mureika |first2=C. C. |last2=Dyer |first3=G. C. |last3=Cupchik |title=Multifractal Structure in Nonrepresentational Art |journal=Physical Review E |volume=72 |issue=4 |pages=046101–1–15 |year=2005 |doi=10.1103/PhysRevE.72.046101|pmid=16383462 |arxiv=physics/0506063 |bibcode=2005PhRvE..72d6101M }}</ref><ref>{{cite journal |first1=C. |last1=Redies |first2=J. |last2=Hasenstein |first3=J. |last3=Denzler |title=Fractal-Like Image Statistics in Visual Art: Similarity to Natural Scenes |journal=Spatial Vision |volume=21 |issue=1 |pages=137–148 |year=2007 |doi=10.1163/156856807782753921|pmid=18073055 }}</ref><ref>{{cite journal |first1=S. |last1=Lee |first2=S. |last2=Olsen |first3=B. |last3=Gooch |title=Simulating and Analyzing Jackson Pollock's Paintings |journal=Journal of Mathematics and the Arts |volume=1 |issue=2 |pages=73–83 |year=2007 |doi=10.1080/17513470701451253|citeseerx=10.1.1.141.7470 }}</ref><ref>{{cite journal |first1=J. |last1=Alvarez-Ramirez |first2=C. |last2=Ibarra-Valdez |first3=E. |last3=Rodriguez |first4=L. |last4=Dagdug |title=1/f-Noise Structure in Pollock's Drip Paintings |journal=Physica A |volume=387 |issue=1 |pages=281–295 |year=2008 |doi=10.1016/j.physa.2007.08.047|bibcode=2008PhyA..387..281A }}</ref><ref>{{cite journal |first1=D. J. |last1=Graham |first2=D. J. |last2=Field |title=Variations in Intensity for Representative and Abstract Art, and for Art from Eastern and Western Hemispheres |journal=Perception |volume=37 |issue=9 |pages=1341–1352 |year=2008 |doi=10.1068/p5971|pmid=18986061 |url=http://redwood.psych.cornell.edu/papers/graham-field-perception-2008.pdf |citeseerx=10.1.1.193.4596 }}</ref><ref>{{cite journal |first1=J. |last1=Alvarez-Ramirez |first2=J. C. |last2=Echeverria |first3=E. |last3=Rodriguez |title=Performance of a high-dimensional R/S method for Hurst exponent estimation |journal=Physica A |volume=387 |issue=26 |pages=6452–6462 |year=2008 |doi=10.1016/j.physa.2008.08.014|bibcode=2008PhyA..387.6452A }}</ref><ref>{{cite journal |first1=J. |last1=Coddington |first2=J. |last2=Elton |first3=D. |last3=Rockmore |first4=Y. |last4=Wang |title=Multifractal Analysis and Authentication of Jackson Pollock Paintings |journal=Proceedings of SPIE |volume=6810 |issue=68100F |pages=1–12 |year=2008 |doi=10.1117/12.765015|bibcode=2008SPIE.6810E..0FC }}</ref><ref>{{cite journal |first1=M. |last1=Al-Ayyoub |first2=M. T. |last2=Irfan |first3=D. G. |last3=Stork |title=Boosting Multi-Feature Visual Texture Classifiers for the Authentification of Jackson Pollock's Drip Paintings |journal=SPIE Proceedings on Computer Vision and Image Analysis of Art II |volume=7869 |issue=78690H |pages=78690H |year=2009 |doi=10.1117/12.873142|series=Computer Vision and Image Analysis of Art II |bibcode=2011SPIE.7869E..0HA }}</ref><ref>{{cite journal |first1=J. R. |last1=Mureika |first2=R. P. |last2=Taylor |title=The Abstract Expressionists and Les Automatistes: multi-fractal depth? |journal=Signal Processing |volume=93 |issue=3 |page=573 |year=2013 |doi=10.1016/j.sigpro.2012.05.002}}</ref><ref>{{cite journal |first1=R. P. |last1=Taylor |display-authors=etal |title=Authenticating Pollock Paintings Using Fractal Geometry |journal=Pattern Recognition Letters |volume=28 |issue=6 |pages=695–702 |year=2005 |doi=10.1016/j.patrec.2006.08.012}}</ref><ref>{{cite journal |first1=K. |last1=Jones-Smith |display-authors=etal |title=Fractal Analysis: Revisiting Pollock's Paintings |journal=Nature |volume=444 |issue=7119 |pages=E9–10 |year=2006 |doi=10.1038/nature05398|pmid=17136047 |bibcode=2006Natur.444E...9J }}</ref><ref>{{cite journal |first1=R. P. |last1=Taylor |display-authors=etal |title=Fractal Analysis: Revisiting Pollock's Paintings (Reply)|journal=Nature |volume=444 |issue=7119 |pages=E10–11 |year=2006 |doi=10.1038/nature05399|bibcode=2006Natur.444E..10T }}</ref>分形分析后来被用来区分 Jackson Pollock 的真品和赝品，辨认成功率达到了93% 。<ref>{{cite journal |first1=L. |last1=Shamar |title=What Makes a Pollock Pollock: A Machine Vision Approach |journal=International Journal of Arts and Technology |volume=8 |pages=1–10 |year=2015 |doi=10.1504/IJART.2015.067389|url=http://vfacstaff.ltu.edu/lshamir/publications/wm_pollock.pdf |citeseerx=10.1.1.647.365 }}</ref>认知神经科学家已经证实，Jackson Pollock的分形可以像计算机生成的分形和自然分形一样，减少观察者的识别难度。<ref>{{cite journal |first1=R. P. |last1=Taylor |first2=B. |last2=Spehar |first3=P. |last3=Van Donkelaar |first4=C. M. |last4=Hagerhall |title=Perceptual and Physiological Responses to Jackson Pollock's Fractals |journal=Frontiers in Human Neuroscience |volume=5 |pages=1–13 |year=2011 |doi=10.3389/fnhum.2011.00060|pmid=21734876 |pmc=3124832 }}</ref>

自1999年以来，超过10个科学团队对杰克逊·波洛克 Jackson Pollock(1912-1956)的50多幅油画进行了分形分析，这些油画是直接将颜料倒在水平画布上创作出来的。<ref>{{cite journal |first=R. P. |last=Taylor |display-authors=etal |title=Fractal Analysis of Pollock's Drip Paintings |journal=Nature |volume=399 |issue=6735 |page=422 |year=1999|bibcode=1999Natur.399..422T |doi=10.1038/20833 }}</ref><ref>{{cite journal |first1=J. R. |last1=Mureika |first2=C. C. |last2=Dyer |first3=G. C. |last3=Cupchik |title=Multifractal Structure in Nonrepresentational Art |journal=Physical Review E |volume=72 |issue=4 |pages=046101–1–15 |year=2005 |doi=10.1103/PhysRevE.72.046101|pmid=16383462 |arxiv=physics/0506063 |bibcode=2005PhRvE..72d6101M }}</ref><ref>{{cite journal |first1=C. |last1=Redies |first2=J. |last2=Hasenstein |first3=J. |last3=Denzler |title=Fractal-Like Image Statistics in Visual Art: Similarity to Natural Scenes |journal=Spatial Vision |volume=21 |issue=1 |pages=137–148 |year=2007 |doi=10.1163/156856807782753921|pmid=18073055 }}</ref><ref>{{cite journal |first1=S. |last1=Lee |first2=S. |last2=Olsen |first3=B. |last3=Gooch |title=Simulating and Analyzing Jackson Pollock's Paintings |journal=Journal of Mathematics and the Arts |volume=1 |issue=2 |pages=73–83 |year=2007 |doi=10.1080/17513470701451253|citeseerx=10.1.1.141.7470 }}</ref><ref>{{cite journal |first1=J. |last1=Alvarez-Ramirez |first2=C. |last2=Ibarra-Valdez |first3=E. |last3=Rodriguez |first4=L. |last4=Dagdug |title=1/f-Noise Structure in Pollock's Drip Paintings |journal=Physica A |volume=387 |issue=1 |pages=281–295 |year=2008 |doi=10.1016/j.physa.2007.08.047|bibcode=2008PhyA..387..281A }}</ref><ref>{{cite journal |first1=D. J. |last1=Graham |first2=D. J. |last2=Field |title=Variations in Intensity for Representative and Abstract Art, and for Art from Eastern and Western Hemispheres |journal=Perception |volume=37 |issue=9 |pages=1341–1352 |year=2008 |doi=10.1068/p5971|pmid=18986061 |url=http://redwood.psych.cornell.edu/papers/graham-field-perception-2008.pdf |citeseerx=10.1.1.193.4596 }}</ref><ref>{{cite journal |first1=J. |last1=Alvarez-Ramirez |first2=J. C. |last2=Echeverria |first3=E. |last3=Rodriguez |title=Performance of a high-dimensional R/S method for Hurst exponent estimation |journal=Physica A |volume=387 |issue=26 |pages=6452–6462 |year=2008 |doi=10.1016/j.physa.2008.08.014|bibcode=2008PhyA..387.6452A }}</ref><ref>{{cite journal |first1=J. |last1=Coddington |first2=J. |last2=Elton |first3=D. |last3=Rockmore |first4=Y. |last4=Wang |title=Multifractal Analysis and Authentication of Jackson Pollock Paintings |journal=Proceedings of SPIE |volume=6810 |issue=68100F |pages=1–12 |year=2008 |doi=10.1117/12.765015|bibcode=2008SPIE.6810E..0FC }}</ref><ref>{{cite journal |first1=M. |last1=Al-Ayyoub |first2=M. T. |last2=Irfan |first3=D. G. |last3=Stork |title=Boosting Multi-Feature Visual Texture Classifiers for the Authentification of Jackson Pollock's Drip Paintings |journal=SPIE Proceedings on Computer Vision and Image Analysis of Art II |volume=7869 |issue=78690H |pages=78690H |year=2009 |doi=10.1117/12.873142|series=Computer Vision and Image Analysis of Art II |bibcode=2011SPIE.7869E..0HA }}</ref><ref>{{cite journal |first1=J. R. |last1=Mureika |first2=R. P. |last2=Taylor |title=The Abstract Expressionists and Les Automatistes: multi-fractal depth? |journal=Signal Processing |volume=93 |issue=3 |page=573 |year=2013 |doi=10.1016/j.sigpro.2012.05.002}}</ref><ref>{{cite journal |first1=R. P. |last1=Taylor |display-authors=etal |title=Authenticating Pollock Paintings Using Fractal Geometry |journal=Pattern Recognition Letters |volume=28 |issue=6 |pages=695–702 |year=2005 |doi=10.1016/j.patrec.2006.08.012}}</ref><ref>{{cite journal |first1=K. |last1=Jones-Smith |display-authors=etal |title=Fractal Analysis: Revisiting Pollock's Paintings |journal=Nature |volume=444 |issue=7119 |pages=E9–10 |year=2006 |doi=10.1038/nature05398|pmid=17136047 |bibcode=2006Natur.444E...9J }}</ref><ref>{{cite journal |first1=R. P. |last1=Taylor |display-authors=etal |title=Fractal Analysis: Revisiting Pollock's Paintings (Reply)|journal=Nature |volume=444 |issue=7119 |pages=E10–11 |year=2006 |doi=10.1038/nature05399|bibcode=2006Natur.444E..10T }}</ref>分形分析后来被用来区分 Jackson Pollock 的真品和赝品，辨认成功率达到了93% 。<ref>{{cite journal |first1=L. |last1=Shamar |title=What Makes a Pollock Pollock: A Machine Vision Approach |journal=International Journal of Arts and Technology |volume=8 |pages=1–10 |year=2015 |doi=10.1504/IJART.2015.067389|url=http://vfacstaff.ltu.edu/lshamir/publications/wm_pollock.pdf |citeseerx=10.1.1.647.365 }}</ref>认知神经科学家已经证实，Jackson Pollock的分形可以像计算机生成的分形和自然分形一样，减少观察者的识别难度。<ref>{{cite journal |first1=R. P. |last1=Taylor |first2=B. |last2=Spehar |first3=P. |last3=Van Donkelaar |first4=C. M. |last4=Hagerhall |title=Perceptual and Physiological Responses to Jackson Pollock's Fractals |journal=Frontiers in Human Neuroscience |volume=5 |pages=1–13 |year=2011 |doi=10.3389/fnhum.2011.00060|pmid=21734876 |pmc=3124832 }}</ref>