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词条 Fractal analysis
释义

  1. Types of fractal analysis

  2. Applications

  3. See also

  4. References

  5. Further reading

Fractal analysis is assessing fractal characteristics of data. It consists of several methods to assign a fractal dimension and other fractal characteristics to a dataset which may be a theoretical dataset or a pattern or signal extracted from phenomena including natural geometric objects, sound, market fluctuations,[1][2][3] heart rates,[4] frequency domain in Electroencephalography signals,[5][6] digital images,[7] molecular motion, networks, etc.

Fractal analysis is now widely used in all areas of science.[8] An important limitation of fractal analysis is that arriving at an empirically determined fractal dimension does not necessarily prove that a pattern is fractal; rather, other essential characteristics have to be considered.[9]

Types of fractal analysis

Several types of fractal analysis are done, including box counting, lacunarity analysis, mass methods, and multifractal analysis.[1][9] A common feature of all types of fractal analysis is the need for benchmark patterns against which to assess outputs.[10] These can be acquired with various types of fractal generating software capable of generating benchmark patterns suitable for this purpose, which generally differ from software designed to render fractal art.

Applications

Applications of fractal analysis include:[11]

{{col-start}}{{col-break}}
  • Heart rate analysis[4]
  • Human gait, balance, and activity[12][13]
  • Diagnostic imaging [17]
  • Cancer research [14]
  • Classification of histopathology slides in medicine[15]
  • Fractal landscape or Coastline complexity[9][16]
  • Electrical Engineering[17]
  • Enzyme/enzymology (Michaelis-Menten kinetics)[18]
  • Generation of new music
  • Generation of various art forms
  • Detecting ‘life as we don't know it’ by fractal analysis
  • Search and rescue[19]
  • Signal and image compression
{{Col-break}}{{col-break}}
  • Urban growth[20]
  • Neuroscience[21][22][23][24]
  • Diagnostic imaging[25]
  • Pathology[26][27][28]
  • Geology[29]
  • Geography[20]
  • Archaeology[30][31]
  • Seismology[32][33]
  • [https://arxiv.org/abs/0904.0780 Wave propagation in self-similar (fractal) media]
  • Soil studies[34]
{{col-break}}
  • Computer and video game design, especially computer graphics for organic environments and as part of procedural generation
  • Fractography and fracture mechanics
  • Fractal antennas — Small size antennas using fractal shapes
  • Small angle scattering theory of fractally rough systems
  • T-shirts and other fashion
  • Generation of patterns for camouflage, such as MARPAT
  • Digital sundial
  • Technical analysis of price series (see Elliott wave principle)
  • Fractal analysis in music[35]
{{col-end}}

See also

  • Multifractal
  • Rescaled range

References

1. ^1 {{cite book | last = Peters | first = Edgar | title = Chaos and order in the capital markets : a new view of cycles, prices, and market volatility | publisher = Wiley | location = New York | year = 1996 | isbn = 978-0-471-13938-6 }}
2. ^{{cite journal | last = Mulligan | first = R. | title = Fractal analysis of highly volatile markets: an application to technology equities| journal = The Quarterly Review of Economics and Finance | year = 2004 | doi=10.1016/S1062-9769(03)00028-0 | volume=44 | pages=155–179}}
3. ^{{cite journal | last = Kamenshchikov | first = S. | title = Transport Catastrophe Analysis as an Alternative to a Monofractal Description: Theory and Application to Financial Crisis Time Series| journal = Journal of Chaos | year = 2014 | doi=10.1155/2014/346743 | volume=2014 | pages=1–8}}
4. ^1 {{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 = 3929–3941 | year = 2009 | pmid = 19528254| pmc = 2746620}}
5. ^{{Cite journal | last1 = Zappasodi | first1 = Filippo | last2 = Olejarczyk | first2 = Elzbieta | last3 = Marzetti | first3 = Laura | last4 = Assenza | first4 = Giovanni | title = Fractal Dimension of EEG Activity Senses Neuronal Impairment in Acute Stroke | doi = 10.1371/journal.pone.0100199 | journal = PLOS ONE | volume = 9 | issue = 6 | pages = 3929–3941 | year = 2014 | pmid = 24967904| pmc = 4072666| bibcode = 2014PLoSO...9j0199Z }}
6. ^{{Cite book | last1 = Hisonothai | first1 = M. | last2 = Nakagawa | first2 = M. | title = EEG signal classification method based on fractal features and neural network | doi = 10.1109/IEMBS.2008.4650057 | journal = MEDLINE-Annual International Conference of the IEEE Engineering in Medicine and Biology Society | year = 2008 | pmid = 19163560 | volume=2008 | pages=3880–3| isbn = 978-1-4244-1814-5 }}
7. ^Fractal Analysis of Digital Images http://rsbweb.nih.gov/ij/plugins/fraclac/FLHelp/Fractals.htm
8. ^{{cite journal|title=Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society | url=http://www.worldscinet.com/fractals/fractals.shtml|issn=1793-6543}}
9. ^1 2 {{cite book|author=Benoît B. Mandelbrot|title=The fractal geometry of nature|url=https://books.google.com/books?id=0R2LkE3N7-oC|accessdate=1 February 2012|year=1983|publisher=Macmillan|isbn=978-0-7167-1186-5}}
10. ^{{Cite document|title=Digital Images in FracLac |publisher=ImageJ |accessdate=2012-02-08 |url=http://rsbweb.nih.gov/ij/plugins/fraclac/FLHelp/Images.htm |postscript={{inconsistent citations}} |deadurl=bot: unknown |archiveurl=https://www.webcitation.org/65J0FscOz?url=http://rsbweb.nih.gov/ij/plugins/fraclac/FLHelp/Images.htm |archivedate=2012-02-08 |df= }}
11. ^{{cite web|url=http://library.thinkquest.org/26242/full/ap/ap.html|title=Applications|accessdate=2007-10-21|deadurl=yes|archiveurl=https://web.archive.org/web/20071012223212/http://library.thinkquest.org/26242/full/ap/ap.html|archivedate=2007-10-12|df=}}
12. ^{{Cite journal|last=Costa|first=Isis da Silva|last2=Gamundí|first2=Antoni|last3=Miranda|first3=José G. Vivas|last4=França|first4=Lucas G. Souza|last5=Santana|first5=De|last6=Novaes|first6=Charles|last7=Montoya|first7=Pedro|date=2017|title=Altered Functional Performance in Patients with Fibromyalgia|journal=Frontiers in Human Neuroscience|language=English|volume=11|pages=14|doi=10.3389/fnhum.2017.00014|pmid=28184193|pmc=5266716|issn=1662-5161}}
13. ^{{cite journal |last1=França |first1=L. G. S. |last2=Montoya |first2=Pedro |last3=Miranda |first3=J. G. V.|date=2017 |title=On multifractals: a non-linear study of actigraphy data |journal=Physica A: Statistical Mechanics and its Applications |volume=514 |pages=612–619 |arxiv=1702.03912|doi=10.1016/j.physa.2018.09.122 }}
14. ^{{Cite journal | last1 = Kam | first1 = Y. | last2 = Karperien | first2 = A. | last3 = Weidow | first3 = B. | last4 = Estrada | first4 = L. | last5 = Anderson | first5 = A. R. | last6 = Quaranta | first6 = V. | doi = 10.1186/1756-0500-2-130 | title = Nest expansion assay: A cancer systems biology approach to in vitro invasion measurements | journal = BMC Research Notes | volume = 2 | pages = 130 | year = 2009 | pmid = 19594934| pmc =2716356 }}
15. ^{{cite book|editor1-last = Losa|editor1-first= Gabriele A.|editor2-last= Nonnenmacher|editor2-first= Theo F.|title=Fractals in biology and medicine|url=https://books.google.com/books?id=t9l9GdAt95gC|accessdate=1 February 2012|year=2005|publisher=Springer|isbn=978-3-7643-7172-2}}
16. ^{{Cite journal | last1 = Mandelbrot | first1 = B. | title = How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension | doi = 10.1126/science.156.3775.636 | journal = Science | volume = 156 | issue = 3775 | pages = 636–638 | year = 1967 | pmid = 17837158| pmc = |bibcode = 1967Sci...156..636M }}
17. ^{{Cite journal | last1 = Li | first1 = H. | title = Fractal analysis of side channels for breakdown structures in XLPE cable insulation | doi = 10.1007/s10854-012-0988-y | journal = J Mater Sci: Mater Electron | volume = 24 | issue = 5 | pages = 1640–1643 | year = 2013 }}
18. ^{{cite journal|last1=Reuveni|first1=Shlomi|last2=Granek|first2=Rony|last3=Klafter|first3=Joseph|title=Proteins: Coexistence of Stability and Flexibility|journal=Physical Review Letters|volume=100|issue=20|pages=208101|year=2008|issn=0031-9007|doi=10.1103/PhysRevLett.100.208101|pmid=18518581|bibcode=2008PhRvL.100t8101R}}
19. ^{{cite book| title=An Algorithmic Approach to Generate After-disaster Test Fields for Search and Rescue Agents| author=Panteha Saeedi, and Soren A. Sorensen | journal=Proceedings of the World Congress on Engineering 2009 |pages=93–98 | isbn=978-988-17-0125-1|url=http://www.iaeng.org/publication/WCE2009/WCE2009_pp93-98.pdf}}
20. ^1 {{Cite journal | last1 = Chen | first1 = Yanguang | title = Modeling Fractal Structure of City-Size Distributions Using Correlation Functions | doi = 10.1371/journal.pone.0024791 | journal = PLoS ONE | volume = 6 | issue = 9 | pages = e24791 | year = 2011 | pmid = 21949753 | pmc = 3176775|arxiv = 1104.4682 |bibcode = 2011PLoSO...624791C }}
21. ^{{Cite journal | last1 = Karperien | first1 = Audrey L. | last2 = Jelinek | first2 = Herbert F. | last3 = Buchan | first3 = Alastair M. | doi = 10.1142/S0218348X08003880 | title = Box-Counting Analysis of Microglia Form in Schizophrenia, Alzheimer's Disease and Affective Disorder | journal = Fractals | volume = 16 | issue = 2 | pages = 103–107 | year = 2008 | pmid = | pmc = }}
22. ^{{Cite journal|last=França|first=Lucas G. Souza|last2=Miranda|first2=José G. Vivas|last3=Leite|first3=Marco|last4=Sharma|first4=Niraj K.|last5=Walker|first5=Matthew C.|last6=Lemieux|first6=Louis|last7=Wang|first7=Yujiang|date=2018|title=Fractal and Multifractal Properties of Electrographic Recordings of Human Brain Activity: Toward Its Use as a Signal Feature for Machine Learning in Clinical Applications|journal=Frontiers in Physiology|language=English|volume=9|pages=1767|doi=10.3389/fphys.2018.01767|pmid=30618789|pmc=6295567|issn=1664-042X}}
23. ^{{Cite journal | last1 = Liu | first1 = Jing Z. | last2 = Zhang | first2 = Lu D. | last3 = Yue | first3 = Guang H. | doi = 10.1016/S0006-3495(03)74817-6 | title = Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging | journal = Biophysical Journal | volume = 85 | issue = 6 | pages = 4041–4046 | year = 2003 | pmid = 14645092 | pmc = 1303704|bibcode = 2003BpJ....85.4041L }}
24. ^{{cite journal | last1 = Nikolić | first1 = D. | last2 = Moca | first2 = V.V. | last3 = Singer | first3 = W. | last4 = Mureşan | first4 = R.C. | year = 2008 | title = Properties of multivariate data investigated by fractal dimensionality | url = | journal = Journal of Neuroscience Methods | volume = 172 | issue = 1| pages = 27–33 | doi=10.1016/j.jneumeth.2008.04.007| pmid = 18495248 }}
25. ^1 {{Cite journal | last1 = Karperien | first1 = Audrey | last2 = Jelinek | first2 = Herbert F. | last3 = Leandro | first3 = Jorge de Jesus Gomes| last4 = Soares | first4 = João V. B. | last5 = Cesar Jr | first5 = Roberto M. | last6 = Luckie | first6 = Alan | title = Automated detection of proliferative retinopathy in clinical practice | journal = Clinical Ophthalmology (Auckland, N.Z.) | volume = 2 | issue = 1 | pages = 109–122 | year = 2008 | pmid = 19668394 | pmc = 2698675| doi = 10.2147/OPTH.S1579}}
26. ^{{Cite journal | last1 = Smith | first1 = Robert F. | last2 = Mohr | first2 = David N. | last3 = Torres | first3 = Vicente E. | last4 = Offord | first4 = Kenneth P. | last5 = Melton III | first5 = L. Joseph | title = Renal insufficiency in community patients with mild asymptomatic microhematuria | journal = Mayo Clinic Proceedings | volume = 64 | issue = 4 | pages = 409–414 | year = 1989 | pmid = 2716356 | doi=10.1016/s0025-6196(12)65730-9}}
27. ^{{cite journal|author=Al-Kadi O.S, Watson D.|title=Texture Analysis of Aggressive and non-Aggressive Lung Tumor CE CT Images|url=http://sro.sussex.ac.uk/1919/1/tbme.pdf| journal=IEEE Transactions on Biomedical Engineering|volume=55 |issue=7|pages=1822–1830 |year=2008|doi=10.1109/tbme.2008.919735|pmid=18595800}}
28. ^{{Cite journal | last1 = Landini | first1 = Gabriel | title = Fractals in microscopy | doi = 10.1111/j.1365-2818.2010.03454.x | journal = Journal of Microscopy | volume = 241 | issue = 1 | pages = 1–8 | year = 2011 | pmid = 21118245| pmc = }}
29. ^{{Cite journal | last1 = Cheng | first1 = Qiuming | authorlink = Qiuming Cheng| title = Multifractal Modeling and Lacunarity Analysis | journal = Mathematical Geology | volume = 29 | issue = 7 | pages = 919–932 | doi = 10.1023/A:1022355723781 | year = 1997 | pmid = | pmc = }}
30. ^{{Cite journal | last1 = Burkle-Elizondo | first1 = Gerardo | last2 = Valdéz-Cepeda | first2 = Ricardo David | title = Fractal analysis of Mesoamerican pyramids | journal = Nonlinear Dynamics, Psychology, and Life Sciences | volume = 10 | issue = 1 | pages = 105–122 | year = 2006 | pmid = 16393505}}
31. ^{{Cite journal | last1 = Brown | first1 = Clifford T. | last2 = Witschey | first2 = Walter R. T. | last3 = Liebovitch | first3 = Larry S. | title = The Broken Past: Fractals in Archaeology | doi = 10.1007/s10816-005-2396-6 | journal = Journal of Archaeological Method and Theory | volume = 12 | pages = 37–78 | year = 2005 }}
32. ^{{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 = 413–428 | year = 2007 | pmid = | pmc = |bibcode = 2007E&PSL.262..413V }}
33. ^{{cite book|pages=128–140|title=Critical phenomena in natural sciences: chaos, fractals, self-organization, and disorder : concepts and tools|author=Didier Sornette|year=2004|publisher=Springer|isbn=978-3-540-40754-6}}
34. ^{{Cite journal | last1 = Hu | first1 = Shougeng | last2 = Cheng | first2 = Qiuming | last3 = Wang | first3 = Le | last4 = Xie | first4 = Shuyun | title = Multifractal characterization of urban residential land price in space and time | doi = 10.1016/j.apgeog.2011.10.016 | journal = Applied Geography | volume = 34 | pages = 161–170 | year = 2012 | pmid = | pmc = }}
35. ^{{Cite journal | last1 = Brothers | first1 = Harlan J. | doi = 10.1142/S0218348X0700337X | title = Structural Scaling in Bach's Cello Suite No. 3 | journal = Fractals | volume = 15 | pages = 89–95 | year = 2007 | pmid = | pmc = | title-link = Cello Suites (Bach) }}

Further reading

  • Fractals and Fractal Analysis
  • Fractal analysis
  • Benoit – Fractal Analysis Software
  • Fractal Analysis Methods for Human Heartbeat and Gait Dynamics
{{Fractals}}

4 : Chaos theory|Dynamical systems|Dimension theory|Fractals
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