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第147行： − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + − + + − +
→具有分形特征的自然现象
自然界中发现的近似分形在可扩展却有限的尺度范围内显示出自相似性。 例如，分形与树叶之间的联系，目前正被用来确定树木中含有多少碳。
自然界中发现的近似分形在可扩展却有限的尺度范围内显示出自相似性。 例如，分形与树叶之间的联系，目前正被用来确定树木中含有多少碳。
已知具有分形特征的现象包括:
已知具有分形特征的现象包括:<ref>"Hunting the Hidden Dimensional". ''Nova''. PBS. WPMB-Maryland. October 28, 2008.</ref>
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*作用性细胞骨架
*作用性细胞骨架<ref>{{Cite journal |last=Sadegh |first=Sanaz |date=2017 |title=Plasma Membrane is Compartmentalized by a Self-Similar Cortical Actin Meshwork |journal=Physical Review X |volume=7 |issue=1 |pages=011031 |doi=10.1103/PhysRevX.7.011031 |pmc=5500227 |pmid=28690919|arxiv=1702.03997 |bibcode=2017PhRvX...7a1031S }}</ref>
*藻类
*藻类
*动物的着色图案
*动物的着色图案
*血管和肺血管
*血管和肺血管<ref name="modeling vasculature" />
*云层和雨量区
*云层和雨量区<ref>{{Cite journal |last=Lovejoy |first=Shaun |date=1982 |title=Area-perimeter relation for rain and cloud areas|journal=Science |volume=216 |issue=4542 |pages=185–187|doi=10.1126/science.216.4542.185|pmid=17736252 |bibcode=1982Sci...216..185L }}</ref>
*海岸线
*海岸线
*陨石坑
*陨石坑
*水晶
*水晶<ref name="crystal">{{cite book |url=https://books.google.com/?id=qZHyqUli9y8C&pg=PA78&dq=crystal+fractals+book#v=onepage&q=crystal%20fractals%20book |page=78 |first1=Alessandra |last1=Carbone |first2=Mikhael |last2=Gromov |first3=Przemyslaw |last3=Prusinkiewicz |title=Pattern formation in biology, vision and dynamics |year=2000 |publisher=World Scientific |isbn=978-981-02-3792-9 }}</ref>
*DNA
*DNA
*地震
*地震<ref name="seismology">{{Cite journal | last1=Vannucchi | first1=Paola | last2=Leoni | first2=Lorenzo | doi=10.1016/j.epsl.2007.07.056 | title=Structural characterization of the Costa Rica décollement: Evidence for seismically-induced fluid pulsing | journal=Earth and Planetary Science Letters | volume=262 | issue=3–4 | pages=413 | year=2007 | pmid= | pmc=|bibcode=2007E&PSL.262..413V }}</ref><ref>{{cite book |pages=128–140 |title=Critical phenomena in natural sciences: chaos, fractals, selforganization, and disorder: concepts and tools |first=Didier |last=Sornette |year=2004 |publisher=Springer |isbn=978-3-540-40754-6 }}</ref>
*断层线
*断层线
*几何光学
*几何光学<ref name="geomopt">{{citation |first=D. |last=Sweet |first2=E. |last2=Ott |first3=J. A. |last3=Yorke |title=Complex topology in Chaotic scattering: A Laboratory Observation |year=1999 |journal=Nature |volume=399 |pages=315 |doi=10.1038/20573 |issue=6734 |bibcode = 1999Natur.399..315S }}</ref>
*心率
*心率<ref name="heart">{{Cite journal | last1=Tan | first1=Can Ozan | last2=Cohen | first2=Michael A. | last3=Eckberg | first3=Dwain L. | last4=Taylor | first4=J. Andrew | title=Fractal properties of human heart period variability: Physiological and methodological implications | doi=10.1113/jphysiol.2009.169219 | journal=The Journal of Physiology | volume=587 | issue=15 | pages=3929 | year=2009 | pmid= 19528254| pmc=2746620}}</ref>
*心音
*心音<ref name="heartrate">{{cite book |first1= Sergey V. |last1=Buldyrev |first2=Ary L. |last2=Goldberger |first3=Shlomo |last3=Havlin |authorlink3=Shlomo Havlin |first4=Chung-Kang |last4=Peng |first5=H. Eugene |last5=Stanley |chapter=Fractals in Biology and Medicine: From DNA to the Heartbeat |year= 1995 |title= Fractals in Science |editor1-first=Armin |editor1-last=Bunde |editor2-first=Shlomo |editor2-last=Havlin |publisher=Springer |chapter-url= http://havlin.biu.ac.il/Shlomo%20Havlin%20books_f_in_s.php }}</ref>
*闪电
*闪电
*山羊角
*山羊角
*山脉
*山脉
*海浪
*海浪<ref name="nature">{{cite book |url=https://books.google.com/?id=l2E4ciBQ9qEC&pg=PA45&dq=lightning+fractals+book#v=onepage&q=lightning%20fractals%20book |pages=44–46 |title=Fractals and chaos: an illustrated course |first=Paul S. |last=Addison |year=1997 |publisher=CRC Press |accessdate=2011-02-05 |isbn=978-0-7503-0400-9 }}</ref>
*菠萝
*菠萝
*心理主观知觉
*心理主观知觉<ref>{{cite web |last=Pincus |first=David |title=The Chaotic Life: Fractal Brains Fractal Thoughts |url=http://www.psychologytoday.com/blog/the-chaotic-life/200909/fractal-brains-fractal-thoughts |work=psychologytoday.com |date=September 2009 }}</ref>
*蛋白质
*蛋白质<ref>{{cite journal|last1=Enright|first1=Matthew B.|last2=Leitner|first2=David M.|title=Mass fractal dimension and the compactness of proteins|journal=Physical Review E|date=January 27, 2005|volume=71|issue=1|pages=011912|doi=10.1103/PhysRevE.71.011912|pmid=15697635|bibcode = 2005PhRvE..71a1912E |url=https://zenodo.org/record/895378}}</ref>
*土星环
*土星环<ref>{{cite book|last1=Takayasu|first1=H.|title=Fractals in the physical sciences|date=1990|publisher=Manchester University Press|location=Manchester|isbn=9780719034343|page=[https://archive.org/details/fractalsinphysic0000taka_s1f9/page/36 36]|url=https://archive.org/details/fractalsinphysic0000taka_s1f9/page/36}}</ref><ref>{{Cite journal|last1=Jun|first1=Li|authorlink2=Martin Ostoja-Starzewski|last2=Ostoja-Starzewski|first2=Martin|title=Edges of Saturn's Rings are Fractal|journal=SpringerPlus|date=April 1, 2015|volume=4,158|pages=158|doi=10.1186/s40064-015-0926-6|pmid=25883885|pmc=4392038}}</ref>
*河网
*河网
*宝塔花菜
*宝塔花菜
*雪花
*雪花<ref name="snowflake">{{cite book
*土壤孔隙
|url=https://books.google.com/?id=aHux78oQbbkC&pg=PA25&dq=snowflake+fractals+book#v=onepage&q=snowflake%20fractals%20book |page=25 |first1=Yves |last1=Meyer |first2=Sylvie |last2=Roques |title=Progress in wavelet analysis and applications: proceedings of the International Conference "Wavelets and Applications", Toulouse, France – June 1992 |year=1993 |publisher=Atlantica Séguier Frontières |accessdate=2011-02-05 |isbn=978-2-86332-130-0 }}</ref>
*湍流表面
*土壤孔隙<ref>Ozhovan M. I., Dmitriev I. E., Batyukhnova O. G. Fractal structure of pores of clay soil. Atomic Energy, 74, 241–243 (1993).</ref>
*湍流表面<ref>{{cite journal |last=Sreenivasan |first=K. R. |first2=C. |last2=Meneveau |title=The Fractal Facets of Turbulence |journal=Journal of Fluid Mechanics |date=1986 |volume=173 |pages=357–386 |doi=10.1017/S0022112086001209 |bibcode=1986JFM...173..357S}}</ref><ref>{{cite journal |last=de Silva |first=C. M. |first2=J. |last2=Philip |first3=K. |last3=Chauhan |first4=C. |last4=Meneveau |first5=I. |last5=Marusic |title=Multiscale Geometry and Scaling of the Turbulent–Nonturbulent Interface in High Reynolds Number Boundary Layers |journal=Phys. Rev. Lett. |date=2013 |volume=111 |issue=6039 |pages=192–196 |doi=10.1126/science.1203223 |pmid=21737736 |bibcode=2011Sci...333..192A}}</ref>
*树木
*树木
*布朗运动(由一维维纳过程产生)
*布朗运动(由一维维纳过程产生)<ref>{{Cite book |first1=Kenneth |last1=Falconer |title=Fractals, A Very Short Introduction |publisher=Oxford University Press |year=2013}}</ref>
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