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===Natural phenomena with fractal features=== {{Further|Patterns in nature}} Approximate fractals found in nature display self-similarity over extended, but finite, scale ranges. The connection between fractals and leaves, for instance, is currently being used to determine how much carbon is contained in trees.<ref>"Hunting the Hidden Dimensional". ''Nova''. PBS. WPMB-Maryland. October 28, 2008.</ref> Phenomena known to have fractal features include: <!-- Please provide citations for these entries, or those lacking them will be removed --> {{div col|colwidth=20em}} * [[Actin cytoskeleton]]<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> * [[Algae]] * [[Animal coloration]] patterns * [[Blood vessel]]s and [[pulmonary vessels]]<ref name="modeling vasculature" /> * Brownian motion (generated by a one-dimensional [[Wiener process]]).<ref>{{Cite book |first1=Kenneth |last1=Falconer |title=Fractals, A Very Short Introduction |publisher=Oxford University Press |year=2013}}</ref> * Clouds and rainfall areas<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 |s2cid=32255821 }}</ref> * Coastlines <ref>{{cite journal | last1=Boffetta | first1=G. | last2=Celani | first2=A. | last3=Dezzani | first3=D. | last4=Seminara | first4=A. | title=How winding is the coast of Britain? Conformal invariance of rocky shorelines | journal=Geophysical Research Letters | volume=35 | issue=3 | date=2008 | issn=0094-8276 | doi=10.1029/2007GL033093 | doi-access=free | arxiv=0712.3076 | bibcode=2008GeoRL..35.3615B }}</ref> * [[Impact crater|Craters]] * Crystals<ref name="crystal">{{cite book |chapter-url=https://books.google.com/books?id=qZHyqUli9y8C&q=crystal+fractals+book&pg=PA78 |first1=James W. |last1=Cannon |first2=William J. |last2=Floyd |first3=Walter R. |last3=Perry |chapter=Crystal growth, biological cell growth and geometry |pages=65–82 |title=Pattern formation in biology, vision and dynamics |year=2000 |publisher=World Scientific |isbn=978-981-02-3792-9 |editor-last1=Carbone|editor-first1=Alessandra|editor-last2=Gromov|editor-first2=Mikhael|editor-last3=Prusinkiewicz|editor-first3=Przemyslaw}}</ref> * [[DNA]] * Dust grains<ref>{{citation|title=Electrification in granular gases leads to constrained fractal growth|author=Singh, Chamkor|author2=Mazza, Marco|journal=Scientific Reports|volume=9|year=2019|issue=1|page=9049|doi=10.1038/s41598-019-45447-x|publisher=Nature Publishing Group|pmid=31227758|pmc=6588598|arxiv=1812.06073|bibcode=2019NatSR...9.9049S|doi-access=free}}</ref> * [[Earthquakes]]<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 |bibcode=2007E&PSL.262..413V | hdl=2158/257208 | s2cid=128467785 | hdl-access=free }}</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> * [[Fault line]]s * Geometrical optics<ref name="geomopt">{{citation |first1=D. |last1=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 |s2cid=4361904 }}</ref> * Heart rates<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=3929–41 | year=2009 | pmid=19528254| pmc=2746620}}</ref> * [[Heart sounds]] * [[Lake]] shorelines and areas<ref>{{cite journal |author1=D. Seekell |author2=B. Cael |author3=E. Lindmark |author4=P. Byström |title=The fractal scaling relationship for river inlets to lakes |journal=Geophysical Research Letters |date=2021 |volume=48 |issue=9 |pages=e2021GL093366 |doi=10.1029/2021GL093366| issn=0094-8276 |bibcode=2021GeoRL..4893366S |s2cid=235508504 |url=http://urn.kb.se/resolve?urn=urn:nbn:se:umu:diva-183511 }}</ref><ref>{{cite journal |author1=D. Seekell |author2=M. L. Pace |author3=L. J. Tranvik |author4=C. Verpoorter |title=A fractal-based approach to lake size-distributions |journal=Geophysical Research Letters |date=2013 |volume=40 |issue=3 |pages=517–521 |doi=10.1002/grl.50139 |bibcode=2013GeoRL..40..517S |s2cid=14482711 |url=https://hal.archives-ouvertes.fr/hal-00932495/file/grl.50139.pdf }}</ref><ref>{{cite journal |author1=B. B. Cael |author2=D. A. Seekell |title=The size-distribution of Earth's lakes |journal=Scientific Reports |date=2016 |volume=6 |pages=29633 |doi=10.1038/srep29633 |pmid=27388607 |pmc=4937396 |bibcode=2016NatSR...629633C }}</ref> * [[Lightning]] bolts * Mountain-goat horns * [[Neuron]]s * Polymers * Percolation * [[Mountain|Mountain ranges]] * [[Wind wave|Ocean waves]]<ref name="nature">{{cite book |url=https://books.google.com/books?id=l2E4ciBQ9qEC&q=lightning+fractals+book&pg=PA45 |pages=44–46 |title=Fractals and chaos: an illustrated course |first=Paul S. |last=Addison |year=1997 |publisher=CRC Press |access-date=February 5, 2011 |isbn=978-0-7503-0400-9 }}</ref> * Pineapple * [[Proteins]]<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> * [[Psychedelic experience]]<ref> {{cite journal |author1=Thomas F. Varley |author2= Robin Carhart-Harris |author3=Leor Roseman |author4=David K. Menon |author5=Emmanuel A. Stamatakis |title=Serotonergic psychedelics LSD & psilocybin increase the fractal dimension of cortical brain activity in spatial and temporal domains |journal=[[NeuroImage]] |volume=220 |year=2020 |doi=10.1016/j.neuroimage.2020.117049}}</ref> *[[Purkinje cell]]s<ref>{{cite journal|last1=Takeda|first1=T|last2=Ishikawa|first2=A|last3=Ohtomo|first3=K|last4=Kobayashi|first4=Y|last5=Matsuoka|first5=T|title=Fractal dimension of dendritic tree of cerebellar Purkinje cell during onto- and phylogenetic development|journal=Neurosci Research|date=February 1992|volume=13|issue=1|pages=19–31|doi=10.1016/0168-0102(92)90031-7|pmid=1314350|s2cid=4158401}}</ref> * [[Rings of Saturn]]<ref>{{cite book|last1=Takayasu|first1=H.|title=Fractals in the physical sciences|date=1990|publisher=Manchester University Press|location=Manchester|isbn=978-0-7190-3434-3|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|author-link2=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 |doi-access=free }}</ref> * [[river|River networks]]<ref>{{cite journal |last1=Tarboton |first1=David G |last2=Bras |first2=Rafael L |last3=Rodriguez-Iturbe |first3=Ignacio |title=The fractal nature of river networks |journal=Water Resources Research |date=1988 |volume=24 |issue=8 |page=1317|doi=10.1029/WR024i008p01317 |bibcode=1988WRR....24.1317T }}</ref> * [[Romanesco broccoli]] * Snowflakes<ref name="snowflake">{{cite book |url=https://books.google.com/books?id=aHux78oQbbkC&q=snowflake+fractals+book&pg=PA25 |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 |access-date=February 5, 2011 |isbn=978-2-86332-130-0 }}</ref> * Soil pores<ref>Ozhovan M. I., Dmitriev I. E., Batyukhnova O. G. Fractal structure of pores of clay soil. Atomic Energy, 74, 241–243 (1993).</ref> *Surfaces in [[Turbulence|turbulent]] flows<ref>{{cite journal |last1=Sreenivasan |first1=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|s2cid=55578215 }}</ref><ref>{{cite journal |last1=de Silva |first1=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|s2cid=22560587 }}</ref> * Trees <ref>{{cite journal |last1=Mandelbrot |first1=Benoit B |title=The fractal geometry of trees and other natural phenomena |journal=Geometrical Probability and Biological Structures: Buffon's 200th Anniversary: Proceedings of the Buffon Bicentenary Symposium on Geometrical Probability, Image Analysis, Mathematical Stereology, and Their Relevance to the Determination of Biological Structures |date=1978 |pages=235–249}}</ref> {{div col end}} <gallery mode="packed" heights="140"> File:Frost patterns 2.jpg|Frost crystals occurring naturally on cold glass form fractal patterns File:Optical Billiard Spheres dsweet.jpeg|Fractal basin boundary in a geometrical optical system<ref name="geomopt"/> File:Glue1 800x600.jpg|A fractal is formed when pulling apart two glue-covered [[Acryloyl group|acrylic]] sheets File:Square1.jpg|High-voltage breakdown within a {{convert|4|in|abbr=on}} block of acrylic glass creates a fractal [[Lichtenberg figure]] File:Romanesco broccoli (Brassica oleracea).jpg|[[Romanesco broccoli]], showing [[self-similar]] form approximating a natural fractal File:Fractal defrosting patterns on Mars.jpg|Fractal defrosting patterns, polar Mars. The patterns are formed by sublimation of frozen CO<sub>2</sub>. Width of image is about a kilometer. File:Brefeldia maxima plasmodium on wood.jpg|[[Slime mold]] ''[[Brefeldia maxima]]'' growing fractally on wood File:Dendrit.jpg|[[Psilomelane]] [[Dendrite (crystal)|dendrite]]s in the [[Solnhofen Limestone]] </gallery>
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