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more random in their behaviour patterns, indicates that there has been an alteration in the functionality of the individual. Using fractal analysis, it is possible to examine the movement sequential complexity of animal behaviour and to determine whether individuals are experiencing deviations from their optimal range, suggesting a change in condition. For example, it has been used to assess welfare of domestic hens, stress in bottlenose dolphins in response to human disturbance, and parasitic infection in
Japanese macaques and sheep. The research is furthering the field of behavioural ecology by simplifying and quantifying very complex relationships. When it comes to animal welfare and
22:
115:(depending on the direction). Whether the view of the fractal is expanding or contracting, the structure remains the same and appears equivalently complex. Fractal analysis uses these underlying properties to help in the understanding and characterization of complex systems. It is also possible to expand the use of fractals to the lack of a single characteristic time scale, or pattern.
206:
mathematically to determine the structure of the forest stand. The use of fractal analysis for understanding structures, and spatial and temporal complexity in biological systems has already been well studied and its use continues to increase in ecological research. Despite its extensive use, it still receives some
230:
Spatial patterns and animal behaviour sequences in fractal time have an optimal complexity range, which can be thought of as the homeostatic state on the spectrum where the complexity sequence should regularly fall. An increase or a loss in complexity, either becoming more stereotypical or conversely
222:
exhibit fractal properties on spatial and temporal scales. Fractal analysis helps in understanding the behaviour of animals and how they interact with their environments on multiple scales in space and time. Various animal movement signatures in their respective environments have been found to
205:
follows the same architecture as the spatial distribution of the trees in the forest, and that the distribution of the trees in the forest shared the same underlying fractal structure as the branches, scaling identically to the point of being able to use the pattern of the trees’ branches
44:
and other fractal characteristics to a dataset which may be a theoretical dataset, or a pattern or signal extracted from phenomena including topography, natural geometric objects, ecology and aquatic sciences, sound, market fluctuations, heart rates, frequency domain in
196:
systems are altered since fractals are able to characterize the natural complexity in such systems. Thus, fractal analysis can help to quantify patterns in nature and to identify deviations from these natural sequences. It helps to improve our overall understanding of
2196:
Cribb, Nardi; Seuront, Laurent (September 2016). "Changes in the behavioural complexity of bottlenose dolphins along a gradient of anthropogenically-impacted environments in South
Australian coastal waters: Implications for conservation and management strategies".
4126:
2100:
Burgunder, Jade; Petrželková, Klára J.; Modrý, David; Kato, Akiko; MacIntosh, Andrew J.J. (August 2018). "Fractal measures in activity patterns: Do gastrointestinal parasites affect the complexity of sheep behaviour?".
1300:
Rutherford, Kenneth M.D.; Haskell, Marie J.; Glasbey, Chris; Jones, R.Bryan; Lawrence, Alistair B. (September 2003). "Detrended fluctuation analysis of behavioural responses to mild acute stressors in domestic hens".
242:
observations that are limited by the counts of behaviours, but is able to delve into the underlying reason for the behaviour. Another important advantage of fractal analysis is the ability to monitor the health of
61:
have to be considered. Fractal analysis is valuable in expanding our knowledge of the structure and function of various systems, and as a potential tool to mathematically assess novel areas of study.
3193:
Smith, Robert F.; Mohr, David N.; Torres, Vicente E.; Offord, Kenneth P.; Melton III, L. Joseph (1989). "Renal insufficiency in community patients with mild asymptomatic microhematuria".
2018:
Viswanathan, G.M; Afanasyev, V; Buldyrev, Sergey V; Havlin, Shlomo; da Luz, M.G.E; Raposo, E.P; Stanley, H.Eugene (June 2001). "Lévy flights search patterns of biological organisms".
235:, fractal analysis makes it possible to identify potential sources of stress on animal behaviour, stressors that may not always be discernible through classical behaviour research.
57:. 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
2989:
Karperien, Audrey L.; Jelinek, Herbert F.; Buchan, Alastair M. (2008). "Box-Counting
Analysis of Microglia Form in Schizophrenia, Alzheimer's Disease and Affective Disorder".
81:
that indicates the degree to which the objects fill the available space. The fractal dimension measures the change in "size" of a fractal set with the changing observational
3018:"Fractal and Multifractal Properties of Electrographic Recordings of Human Brain Activity: Toward Its Use as a Signal Feature for Machine Learning in Clinical Applications"
1873:
Garcia, F.; Carrère, P.; Soussana, J.F.; Baumont, R. (September 2005). "Characterisation by fractal analysis of foraging paths of ewes grazing heterogeneous swards".
1698:
Halley, J. M.; Hartley, S.; Kallimanis, A. S.; Kunin, W. E.; Lennon, J. J.; Sgardelis, S. P. (2004-02-24). "Uses and abuses of fractal methodology in ecology".
1577:
Morse, D. R.; Lawton, J. H.; Dodson, M. M.; Williamson, M. H. (April 1985). "Fractal dimension of vegetation and the distribution of arthropod body lengths".
1377:
Hastings, Harold M.; Pekelney, Richard; Monticciolo, Richard; Vun Kannon, David; Del Monte, Diane (January 1982). "Time scales, persistence and patchiness".
1531:
456:
62:
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Vannucchi, Paola; Leoni, Lorenzo (2007). "Structural characterization of the Costa Rica décollement: Evidence for seismically-induced fluid pulsing".
1051:
Goldberger, Ary L; Peng, C.-K; Lipsitz, Lewis A (January 2002). "What is physiologic complexity and how does it change with aging and disease?".
1628:
Li, Xiaoyan; Passow, Uta; Logan, Bruce E (January 1998). "Fractal dimensions of small (15–200 μm) particles in
Eastern Pacific coastal waters".
3505:
Hu, Shougeng; Cheng, Qiuming; Wang, Le; Xie, Shuyun (2012). "Multifractal characterization of urban residential land price in space and time".
2887:
Panteha Saeedi, and Soren A. Sorensen (2009). "An
Algorithmic Approach to Generate After-disaster Test Fields for Search and Rescue Agents".
2427:
Costa, Isis da Silva; Gamundí, Antoni; Miranda, José G. Vivas; França, Lucas G. Souza; Santana, De; Novaes, Charles; Montoya, Pedro (2017).
201:
and to reveal some of the underlying structural mechanisms of nature. For example, it was found that the structure of an individual tree’s
3016:
França, Lucas G. Souza; Miranda, José G. Vivas; Leite, Marco; Sharma, Niraj K.; Walker, Matthew C.; Lemieux, Louis; Wang, Yujiang (2018).
1098:
652:"Transport Catastrophe Analysis as an Alternative to a Monofractal Description: Theory and Application to Financial Crisis Time Series"
2534:
Karperien, Audrey; Jelinek, Herbert F.; Leandro, Jorge de Jesus Gomes; Soares, João V. B.; Cesar Jr, Roberto M.; Luckie, Alan (2008).
2273:
Alados, C.L.; Escos, J.M.; Emlen, J.M. (February 1996). "Fractal structure of sequential behaviour patterns: an indicator of stress".
3150:
Nikolić, D.; Moca, V.V.; Singer, W.; Mureşan, R.C. (2008). "Properties of multivariate data investigated by fractal dimensionality".
4144:
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Raposo, E P; Buldyrev, S V; da Luz, M G E; Viswanathan, G M; Stanley, H E (2009-10-30). "Lévy flights and random searches".
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capable of generating benchmark patterns suitable for this purpose, which generally differ from software designed to render
163:. It is suggested to use more than one approach in order to compare results and increase the robustness of one's findings.
1219:
Scheuring, István; Riedi, Rudolf H. (August 1994). "Application of multifractals to the analysis of vegetation pattern".
2728:
975:
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França, L. G. S.; Montoya, Pedro; Miranda, J. G. V. (2017). "On multifractals: a non-linear study of actigraphy data".
791:
Hisonothai, M.; Nakagawa, M. (2008). "EEG signal classification method based on fractal features and neural network".
224:
3623:
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Brown, Clifford T.; Witschey, Walter R. T.; Liebovitch, Larry S. (2005). "The Broken Past: Fractals in
Archaeology".
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1204:
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systems are sources of heterogeneity and generate complex space-time structures that may only demonstrate partial
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MacIntosh, Andrew J. J.; Pelletier, Laure; Chiaradia, Andre; Kato, Akiko; Ropert-Coudert, Yan (December 2013).
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values. This is possible given that a smaller section of the fractal resembles the entirety, showing the same
4006:
3963:
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2828:
Reuveni, Shlomi; Granek, Rony; Klafter, Joseph (2008). "Proteins: Coexistence of
Stability and Flexibility".
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demonstrate spatially non-linear fractal patterns. This has generated ecological interpretations such as the
3482:
Critical phenomena in natural sciences: chaos, fractals, self-organization, and disorder: concepts and tools
3373:
Burkle-Elizondo, Gerardo; Valdéz-Cepeda, Ricardo David (2006). "Fractal analysis of
Mesoamerican pyramids".
3879:
623:
Mulligan, R. (2004). "Fractal analysis of highly volatile markets: an application to technology equities".
4084:
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329:
148:
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Li, H. (2013). "Fractal analysis of side channels for breakdown structures in XLPE cable insulation".
927:
4209:
3816:
2380:"Fractal properties of human heart period variability: Physiological and methodological implications"
1806:
Catalan, Jordi; Marrasé, Cèlia; Pueyo, Salvador; Peters, Francesc; Bartumeus, Frederic (2003-10-28).
685:"Fractal properties of human heart period variability: Physiological and methodological implications"
382:
308:
501:
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2308:
Rutherford, K. M. D.; Haskell, M. J.; Glasbey, C.; Jones, R. B.; Lawrence, A. B. (February 2004).
1420:
West, G. B. (1997-04-04). "A General Model for the Origin of
Allometric Scaling Laws in Biology".
3534:
1808:"Helical Lévy walks: Adjusting searching statistics to resource availability in microzooplankton"
793:
2008 30th Annual
International Conference of the IEEE Engineering in Medicine and Biology Society
314:
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2141:"Fractal analysis of behaviour in a wild primate: behavioural complexity in health and disease"
840:
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181:
46:
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3943:
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1534:(1991). "Fractal Fragmentation, Soil Porosity, and Soil Water Properties: II. Applications".
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403:
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and free-ranging animal populations in their natural habitats without invasive measurements.
140:
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1900:
Humphries, N. E.; Weimerskirch, H.; Queiroz, N.; Southall, E. J.; Sims, D. W. (2012-05-08).
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192:. Using fractal analysis, it is possible to analyze and recognize when features of complex
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2587:"Nest expansion assay: A cancer systems biology approach to in vitro invasion measurements"
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Chaos and order in the capital markets: a new view of cycles, prices, and market volatility
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1256:"Spatio-temporal structure of tidally mixed coastal waters: variability and heterogeneity"
227:, which has proven to be a more accurate description of animal movement for some species.
8:
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2729:"How Long is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension"
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976:"How Long Is the Coast of Britain? Statistical Self-Similarity and Fractional Dimension"
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502:"Anisotropic Multifractal Scaling of Mount Lebanon Topography: Approximate Conditioning"
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Kam, Y.; Karperien, A.; Weidow, B.; Estrada, L.; Anderson, A. R.; Quaranta, V. (2009).
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Zappasodi, Filippo; Olejarczyk, Elzbieta; Marzetti, Laura; Assenza, Giovanni (2014).
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2004:
1124:"Temporal fractals in seabird foraging behaviour: diving through the scales of time"
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2922:"Modeling Fractal Structure of City-Size Distributions Using Correlation Functions"
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Lovejoy, S.; Schertzer, D. (May 2006). "Multifractals, cloud radiances and rain".
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Tan, Can Ozan; Cohen, Michael A.; Eckberg, Dwain L.; Taylor, J. Andrew (2009).
1272:
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800:
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Tan, Can Ozan; Cohen, Michael A.; Eckberg, Dwain L.; Taylor, J. Andrew (2009).
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283:
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This approach is more objective than classical behaviour measurements, such as
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4023:
3413:
3351:
3095:"Fractal Dimension in Human Cerebellum Measured by Magnetic Resonance Imaging"
3002:
2806:
2325:
734:"Fractal Dimension of EEG Activity Senses Neuronal Impairment in Acute Stroke"
525:
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against which to assess outputs. These can be acquired with various types of
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82:
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3313:
3256:
3230:"Texture Analysis of Aggressive and non-Aggressive Lung Tumor CE CT Images"
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2413:
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1953:
1859:
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818:
777:
718:
468:
347:
132:
50:
3268:
3214:
2638:"Deciphering the generating rules and functionalities of complex networks"
1441:
1406:
668:
651:
571:
4139:
4059:
3769:
3764:
853:"Fractals: Complex Geometry, Patterns, and Scaling in Nature and Society"
500:
Gerges, Firas; Geng, Xiaolong; Nassif, Hani; Boufadel, Michel C. (2021).
391:
372:
319:
152:
2310:"Fractal analysis of animal behaviour as an indicator of animal welfare"
3992:
3977:
3972:
3953:
3687:
3465:
2552:
2536:"Automated detection of proliferative retinopathy in clinical practice"
2074:
2057:
1354:
1329:
1240:
857:
Fractals: An Interdiscipinary Journal on the Complex Geometry of Nature
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112:
90:
78:
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Frontier, Serge (1987), "Applications of Fractal Theory to Ecology",
367:
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143:. A common feature of all types of fractal analysis is the need for
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2500:
287:
244:
219:
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2938:
2017:
937:
731:
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2139:
MacIntosh, A. J. J.; Alados, C. L.; Huffman, M. A. (2011-10-07).
362:
193:
144:
120:
86:
54:
33:
1465:"A general quantitative theory of forest structure and dynamics"
3867:
2636:
Xiao, Xiongye; Chen, Hanlong; Bogdan, Paul (25 November 2021).
1966:
1121:
426:
185:
65:
was formulated which is a generalization of ordinary calculus.
3557:
Fractal Analysis Methods for Human Heartbeat and Gait Dynamics
2429:"Altered Functional Performance in Patients with Fibromyalgia"
1902:"Foraging success of biological Levy flights recorded in situ"
93:
properties at different scales. This characteristic is termed
2533:
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1299:
296:
202:
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1872:
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841:
http://rsbweb.nih.gov/ij/plugins/fraclac/FLHelp/Fractals.htm
3568:
1576:
420:
399:
37:
3338:(1997). "Multifractal Modeling and Lacunarity Analysis".
2584:
2426:
1805:
564:
Fractals and Multifractals in Ecology and Aquatic Science
3149:
3015:
1463:
West, G. B.; Enquist, B. J.; Brown, J. H. (2009-04-28).
1330:"Fractal Dimension of a Coral Reef at Ecological Scales"
499:
421:
Small angle scattering theory of fractally rough systems
159:
and the Hurst absolute value method, which estimate the
3399:
2693:
Losa, Gabriele A.; Nonnenmacher, Theo F., eds. (2005).
1630:
Deep Sea Research Part I: Oceanographic Research Papers
932:. Singapore: World Scientific Pub Co Inc. p. 328.
131:
There are various types of fractal analysis, including
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2786:
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53:. Fractal analysis is now widely used in all areas of
3192:
2890:
Proceedings of the World Congress on Engineering 2009
2529:
2527:
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Physica A: Statistical Mechanics and Its Applications
2377:
2020:
Physica A: Statistical Mechanics and Its Applications
1050:
682:
2827:
2485:
925:
888:
3292:Landini, Gabriel (2011). "Fractals in microscopy".
3093:Liu, Jing Z.; Zhang, Lu D.; Yue, Guang H. (2003).
2524:
2231:
2199:Journal of Experimental Marine Biology and Ecology
1969:Journal of Physics A: Mathematical and Theoretical
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882:
880:
878:
876:
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790:
3375:Nonlinear Dynamics, Psychology, and Life Sciences
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2232:Bradbury, J. W.; Vehrencamp, S. L. (2014-05-01).
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2272:
1662:
1462:
1327:
1191:, Springer Berlin Heidelberg, pp. 335–378,
180:which can be easily measured and the underlying
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1906:Proceedings of the National Academy of Sciences
1812:Proceedings of the National Academy of Sciences
1469:Proceedings of the National Academy of Sciences
1253:
871:
425:Generation of patterns for camouflage, such as
49:signals, digital images, molecular motion, and
3504:
3434:
2635:
1741:Bryce, R. M.; Sprague, K. B. (December 2012).
1218:
593:
591:
3584:
1627:
649:
625:The Quarterly Review of Economics and Finance
40:. It consists of several methods to assign a
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2195:
1740:
126:
3402:Journal of Archaeological Method and Theory
3366:
3237:IEEE Transactions on Biomedical Engineering
3092:
2915:
2913:
1743:"Revisiting detrended fluctuation analysis"
1529:
588:
3591:
3577:
3428:
3086:
2726:
1087:
973:
417:— Small size antennas using fractal shapes
255:Applications of fractal analysis include:
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3051:
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2965:
2955:
2937:
2720:
2669:
2612:
2602:
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2551:
2499:
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2444:
2403:
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2073:
2056:MacIntosh, Andrew James Jonathan (2014).
2055:
1943:
1925:
1849:
1831:
1782:
1506:
1488:
1353:
1271:
1254:Seuront, Laurent; Lagadeuc, Yvan (1998).
1163:
767:
757:
708:
667:
2910:
2686:
1186:
622:
171:
68:
20:
4145:List of fractals by Hausdorff dimension
3291:
1556:10.2136/sssaj1991.03615995005500050007x
1536:Soil Science Society of America Journal
643:
616:
561:
250:
4192:
2145:Journal of the Royal Society Interface
926:Khalili Golmankhaneh, Alireza (2022).
921:
919:
784:
725:
597:
16:Mathematical technique in data science
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3334:
2371:
2134:
2132:
2095:
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2051:
2049:
1295:
1293:
1291:
1117:
1115:
1046:
1044:
969:
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965:
929:Fractal Calculus and its Applications
676:
495:
493:
3498:
2919:
1419:
557:
555:
553:
551:
276:Fractal analysis of complex networks
258:
119:Further information on the Origins:
99:, and can be further categorized as
3437:Earth and Planetary Science Letters
2234:"Complexity and behavioral ecology"
1328:Bradbury, Rh; Reichelt, Re (1983).
916:
839:Fractal Analysis of Digital Images
795:. Vol. 2008. pp. 3880–3.
213:
13:
3545:Benoit – Fractal Analysis Software
3528:
2792:
2225:
2129:
2090:
2046:
1288:
1180:
1112:
1041:
962:
490:
14:
4226:
4127:How Long Is the Coast of Britain?
1189:Developments in Numerical Ecology
548:
267:Human gait, balance, and activity
3306:10.1111/j.1365-2818.2010.03454.x
2696:Fractals in biology and medicine
2103:Applied Animal Behaviour Science
1875:Applied Animal Behaviour Science
1712:10.1111/j.1461-0248.2004.00568.x
1303:Applied Animal Behaviour Science
3473:
3393:
3328:
3285:
3228:Al-Kadi O.S, Watson D. (2008).
3221:
3152:Journal of Neuroscience Methods
3143:
3009:
2629:
2578:
2479:
2433:Frontiers in Human Neuroscience
2420:
2346:
2301:
2266:
2189:
2011:
1960:
1893:
1866:
1799:
1734:
1691:
1656:
1621:
1570:
1523:
1456:
1413:
1370:
1321:
1247:
1212:
1101:from the original on 2011-10-20
845:
562:Seuront, Laurent (2009-10-12).
320:Generation of various art forms
225:Lévy Flight Foraging hypothesis
166:
4151:The Fractal Geometry of Nature
3484:. Springer. pp. 128–140.
3164:10.1016/j.jneumeth.2008.04.007
2850:10.1103/PhysRevLett.100.208101
2115:10.1016/j.applanim.2018.05.014
1989:10.1088/1751-8113/42/43/434003
1887:10.1016/j.applanim.2005.01.001
1334:Marine Ecology Progress Series
892:The fractal geometry of nature
833:
392:Computer and video game design
157:detrended fluctuation analysis
1:
3535:Fractals and Fractal Analysis
3207:10.1016/s0025-6196(12)65730-9
3119:10.1016/S0006-3495(03)74817-6
2040:10.1016/S0378-4371(01)00057-7
1685:10.1016/j.jhydrol.2005.02.042
1642:10.1016/s0967-0637(97)00058-7
1315:10.1016/S0168-1591(03)00115-1
1221:Journal of Vegetation Science
1065:10.1016/S0197-4580(01)00266-4
974:Mandelbrot, B. (1967-05-05).
889:Benoît B. Mandelbrot (1983).
637:10.1016/S1062-9769(03)00028-0
484:
3598:
3519:10.1016/j.apgeog.2011.10.016
2957:10.1371/journal.pone.0024791
2753:10.1126/science.156.3775.636
2396:10.1113/jphysiol.2009.169219
1434:10.1126/science.276.5309.122
1391:10.1016/0303-2647(82)90043-0
1260:Journal of Plankton Research
1000:10.1126/science.156.3775.636
759:10.1371/journal.pone.0100199
701:10.1113/jphysiol.2009.169219
402:environments and as part of
7:
4167:Chaos: Making a New Science
2795:J Mater Sci: Mater Electron
2510:10.1016/j.physa.2018.09.122
2211:10.1016/j.jembe.2016.03.020
1197:10.1007/978-3-642-70880-0_9
1095:"Digital Images in FracLac"
462:
149:fractal generating software
10:
4231:
3457:10.1016/j.epsl.2007.07.056
2662:10.1038/s41598-021-02203-4
801:10.1109/IEMBS.2008.4650057
650:Kamenshchikov, S. (2014).
25:Fractal branching of trees
4118:
4042:
3991:
3962:
3878:
3848:
3830:
3671:
3606:
3414:10.1007/s10816-005-2396-6
3003:10.1142/S0218348X08003880
2807:10.1007/s10854-012-0988-y
2384:The Journal of Physiology
2326:10.1017/S0962728600014433
689:The Journal of Physiology
526:10.1142/S0218348X21501127
309:Michaelis-Menten kinetics
127:Types of fractal analysis
77:, which are a measure of
59:essential characteristics
3480:Didier Sornette (2004).
3249:10.1109/tbme.2008.919735
3053:10.3389/fphys.2018.01767
2446:10.3389/fnhum.2017.00014
1273:10.1093/plankt/20.7.1387
85:, and is not limited by
3449:2007E&PSL.262..413V
3352:10.1023/A:1022355723781
3195:Mayo Clinic Proceedings
3022:Frontiers in Physiology
2920:Chen, Yanguang (2011).
2830:Physical Review Letters
2727:Mandelbrot, B. (1967).
2604:10.1186/1756-0500-2-130
1927:10.1073/pnas.1121201109
1833:10.1073/pnas.2137243100
1490:10.1073/pnas.0812294106
315:Generation of new music
182:mathematical properties
4159:The Beauty of Fractals
2540:Clinical Ophthalmology
2287:10.1006/anbe.1996.0040
2157:10.1098/rsif.2011.0049
598:Peters, Edgar (1996).
512:(5): 2150112–2153322.
441:Elliott wave principle
303:Electrical engineering
155:. Other types include
47:electroencephalography
26:
3294:Journal of Microscopy
2251:10.1093/beheco/aru014
2058:"The Fractal Primate"
1053:Neurobiology of Aging
572:10.1201/9781420004243
439:of price series (see
404:procedural generation
172:Ecology and evolution
141:multifractal analysis
75:fractional dimensions
69:Underlying principles
24:
4105:Lewis Fry Richardson
4100:Hamid Naderi Yeganeh
3890:Burning Ship fractal
3822:Weierstrass function
3340:Mathematical Geology
1665:Journal of Hydrology
479:Analysis on fractals
251:Applications include
139:, mass methods, and
111:, the latter scaled
3863:Space-filling curve
3840:Multifractal system
3723:Space-filling curve
3708:Sierpinski triangle
3111:2003BpJ....85.4041L
3099:Biophysical Journal
3044:2018arXiv180603889F
2948:2011PLoSO...624791C
2842:2008PhRvL.100t8101R
2745:1967Sci...156..636M
2654:2021NatSR..1122964X
2032:2001PhyA..295...85V
1981:2009JPhA...42Q4003R
1918:2012PNAS..109.7169H
1824:2003PNAS..10012771B
1818:(22): 12771–12775.
1759:2012NatSR...2E.315B
1677:2006JHyd..322...59L
1591:1985Natur.314..731M
1548:1991SSASJ..55.1239R
1481:2009PNAS..106.7040W
1346:1983MEPS...10..169B
1140:2013NatSR...3E1884M
992:1967Sci...156..636M
750:2014PLoSO...9j0199Z
669:10.1155/2014/346743
602:. New York: Wiley.
518:2021Fract..2950112G
307:Enzyme/enzymology (
264:Heart rate analysis
218:Patterns in animal
176:Unlike theoretical
137:lacunarity analysis
36:characteristics of
4090:Aleksandr Lyapunov
4070:Desmond Paul Henry
4034:Self-avoiding walk
4029:Percolation theory
3673:Iterated function
3614:Fractal dimensions
3562:2016-05-06 at the
3550:2008-05-17 at the
2896:. pp. 93–98.
2642:Scientific Reports
2591:BMC Research Notes
2553:10.2147/OPTH.S1579
2238:Behavioral Ecology
2075:10.2354/psj.30.011
1747:Scientific Reports
1355:10.3354/meps010169
1128:Scientific Reports
437:Technical analysis
410:fracture mechanics
353:Diagnostic imaging
270:Diagnostic imaging
145:benchmark patterns
27:
4205:Dynamical systems
4187:
4186:
4133:Coastline paradox
4110:Wacław Sierpiński
4095:Benoit Mandelbrot
4019:Fractal landscape
3927:Misiurewicz point
3832:Strange attractor
3713:Apollonian gasket
3703:Sierpinski carpet
3507:Applied Geography
3491:978-3-540-40754-6
2903:978-988-17-0125-1
2739:(3775): 636–638.
2706:978-3-7643-7172-2
2390:(15): 3929–3941.
2151:(63): 1497–1509.
1912:(19): 7169–7174.
1767:10.1038/srep00315
1585:(6013): 731–733.
1532:Sposito, Garrison
1475:(17): 7040–7045.
1428:(5309): 122–126.
1148:10.1038/srep01884
986:(3775): 636–638.
947:978-981-126-110-7
902:978-0-7167-1186-5
810:978-1-4244-1814-5
695:(15): 3929–3941.
609:978-0-471-13938-6
452:
451:
408:Fractography and
396:computer graphics
334:image compression
325:Search and rescue
293:Fractal landscape
42:fractal dimension
4222:
4210:Dimension theory
4050:Michael Barnsley
3917:Lyapunov fractal
3775:Sierpiński curve
3728:Blancmange curve
3593:
3586:
3579:
3570:
3569:
3540:Fractal analysis
3523:
3522:
3502:
3496:
3495:
3477:
3471:
3470:
3468:
3443:(3–4): 413–428.
3432:
3426:
3425:
3397:
3391:
3390:
3370:
3364:
3363:
3332:
3326:
3325:
3289:
3283:
3282:
3280:
3279:
3273:
3267:. Archived from
3243:(7): 1822–1830.
3234:
3225:
3219:
3218:
3190:
3184:
3183:
3147:
3141:
3140:
3130:
3105:(6): 4041–4046.
3090:
3084:
3083:
3073:
3055:
3037:
3013:
3007:
3006:
2986:
2980:
2979:
2969:
2959:
2941:
2917:
2908:
2907:
2895:
2884:
2878:
2877:
2825:
2819:
2818:
2801:(5): 1640–1643.
2790:
2784:
2783:
2781:
2780:
2771:. Archived from
2724:
2718:
2717:
2715:
2713:
2690:
2684:
2683:
2673:
2633:
2627:
2626:
2616:
2606:
2582:
2576:
2575:
2565:
2555:
2531:
2522:
2521:
2503:
2483:
2477:
2476:
2466:
2448:
2424:
2418:
2417:
2407:
2375:
2369:
2368:
2366:
2365:
2356:. Archived from
2350:
2344:
2343:
2341:
2340:
2305:
2299:
2298:
2275:Animal Behaviour
2270:
2264:
2263:
2253:
2229:
2223:
2222:
2193:
2187:
2186:
2176:
2136:
2127:
2126:
2097:
2088:
2087:
2077:
2062:Primate Research
2053:
2044:
2043:
2015:
2009:
2008:
1964:
1958:
1957:
1947:
1929:
1897:
1891:
1890:
1870:
1864:
1863:
1853:
1835:
1803:
1797:
1796:
1786:
1738:
1732:
1731:
1695:
1689:
1688:
1660:
1654:
1653:
1625:
1619:
1618:
1599:10.1038/314731a0
1574:
1568:
1567:
1527:
1521:
1520:
1510:
1492:
1460:
1454:
1453:
1417:
1411:
1410:
1374:
1368:
1367:
1357:
1325:
1319:
1318:
1297:
1286:
1285:
1275:
1266:(7): 1387–1401.
1251:
1245:
1244:
1216:
1210:
1209:
1184:
1178:
1177:
1167:
1119:
1110:
1109:
1107:
1106:
1091:
1085:
1084:
1048:
1039:
1038:
1036:
1035:
1026:. Archived from
971:
960:
959:
923:
914:
913:
911:
909:
886:
869:
868:
849:
843:
837:
831:
830:
788:
782:
781:
771:
761:
744:(6): 3929–3941.
729:
723:
722:
712:
680:
674:
673:
671:
656:Journal of Chaos
647:
641:
640:
620:
614:
613:
595:
586:
585:
559:
546:
545:
497:
457:Fractal calculus
415:Fractal antennas
259:
214:Animal behaviour
121:Fractal Geometry
96:scale invariance
63:Fractal calculus
30:Fractal analysis
4230:
4229:
4225:
4224:
4223:
4221:
4220:
4219:
4190:
4189:
4188:
4183:
4114:
4065:Felix Hausdorff
4038:
4002:Brownian motion
3987:
3958:
3881:
3874:
3844:
3826:
3817:Pythagoras tree
3674:
3667:
3663:Self-similarity
3607:Characteristics
3602:
3597:
3564:Wayback Machine
3552:Wayback Machine
3531:
3529:Further reading
3526:
3503:
3499:
3492:
3478:
3474:
3433:
3429:
3398:
3394:
3371:
3367:
3333:
3329:
3290:
3286:
3277:
3275:
3271:
3232:
3226:
3222:
3191:
3187:
3148:
3144:
3091:
3087:
3014:
3010:
2987:
2983:
2918:
2911:
2904:
2893:
2885:
2881:
2826:
2822:
2791:
2787:
2778:
2776:
2725:
2721:
2711:
2709:
2707:
2691:
2687:
2634:
2630:
2583:
2579:
2532:
2525:
2484:
2480:
2425:
2421:
2376:
2372:
2363:
2361:
2352:
2351:
2347:
2338:
2336:
2306:
2302:
2271:
2267:
2230:
2226:
2194:
2190:
2137:
2130:
2098:
2091:
2054:
2047:
2016:
2012:
1965:
1961:
1898:
1894:
1871:
1867:
1804:
1800:
1739:
1735:
1700:Ecology Letters
1696:
1692:
1661:
1657:
1626:
1622:
1575:
1571:
1528:
1524:
1461:
1457:
1418:
1414:
1375:
1371:
1326:
1322:
1298:
1289:
1252:
1248:
1233:10.2307/3235975
1217:
1213:
1207:
1185:
1181:
1120:
1113:
1104:
1102:
1093:
1092:
1088:
1049:
1042:
1033:
1031:
972:
963:
948:
924:
917:
907:
905:
903:
887:
872:
851:
850:
846:
838:
834:
811:
789:
785:
730:
726:
681:
677:
648:
644:
621:
617:
610:
596:
589:
582:
560:
549:
498:
491:
487:
465:
453:
432:Digital sundial
273:Cancer research
253:
240:frequency-based
216:
190:self-similarity
174:
169:
129:
113:anisotropically
102:self-similarity
71:
17:
12:
11:
5:
4228:
4218:
4217:
4212:
4207:
4202:
4185:
4184:
4182:
4181:
4176:
4171:
4163:
4155:
4147:
4142:
4137:
4136:
4135:
4122:
4120:
4116:
4115:
4113:
4112:
4107:
4102:
4097:
4092:
4087:
4082:
4080:Helge von Koch
4077:
4072:
4067:
4062:
4057:
4052:
4046:
4044:
4040:
4039:
4037:
4036:
4031:
4026:
4021:
4016:
4015:
4014:
4012:Brownian motor
4009:
3998:
3996:
3989:
3988:
3986:
3985:
3983:Pickover stalk
3980:
3975:
3969:
3967:
3960:
3959:
3957:
3956:
3951:
3946:
3941:
3939:Newton fractal
3936:
3931:
3930:
3929:
3922:Mandelbrot set
3919:
3914:
3913:
3912:
3907:
3905:Newton fractal
3902:
3892:
3886:
3884:
3876:
3875:
3873:
3872:
3871:
3870:
3860:
3858:Fractal canopy
3854:
3852:
3846:
3845:
3843:
3842:
3836:
3834:
3828:
3827:
3825:
3824:
3819:
3814:
3809:
3804:
3802:Vicsek fractal
3799:
3794:
3789:
3784:
3783:
3782:
3777:
3772:
3767:
3762:
3757:
3752:
3747:
3742:
3741:
3740:
3730:
3720:
3718:Fibonacci word
3715:
3710:
3705:
3700:
3695:
3693:Koch snowflake
3690:
3685:
3679:
3677:
3669:
3668:
3666:
3665:
3660:
3655:
3654:
3653:
3648:
3643:
3638:
3633:
3632:
3631:
3621:
3610:
3608:
3604:
3603:
3596:
3595:
3588:
3581:
3573:
3567:
3566:
3554:
3542:
3537:
3530:
3527:
3525:
3524:
3497:
3490:
3472:
3427:
3392:
3381:(1): 105–122.
3365:
3346:(7): 919–932.
3336:Cheng, Qiuming
3327:
3284:
3220:
3201:(4): 409–414.
3185:
3142:
3085:
3008:
2997:(2): 103–107.
2981:
2909:
2902:
2879:
2836:(20): 208101.
2820:
2785:
2719:
2705:
2685:
2628:
2577:
2546:(1): 109–122.
2523:
2478:
2419:
2370:
2354:"Applications"
2345:
2314:Animal Welfare
2300:
2281:(2): 437–443.
2265:
2244:(3): 435–442.
2224:
2188:
2128:
2089:
2045:
2026:(1–2): 85–88.
2010:
1975:(43): 434003.
1959:
1892:
1881:(1–2): 19–37.
1865:
1798:
1733:
1706:(3): 254–271.
1690:
1671:(1–4): 59–88.
1655:
1636:(1): 115–131.
1620:
1569:
1530:Rieu, Michel;
1522:
1455:
1412:
1385:(4): 281–289.
1369:
1320:
1309:(2): 125–139.
1287:
1246:
1227:(4): 489–496.
1211:
1205:
1179:
1111:
1086:
1040:
961:
946:
915:
901:
870:
844:
832:
809:
783:
724:
675:
642:
615:
608:
587:
580:
547:
488:
486:
483:
482:
481:
476:
474:Rescaled range
471:
464:
461:
460:
459:
450:
449:
445:
444:
434:
429:
423:
418:
412:
406:
387:
386:
385:
380:
375:
370:
365:
360:
355:
350:
345:
340:
338:
337:
336:
327:
322:
317:
312:
305:
300:
290:
284:histopathology
280:Classification
277:
274:
271:
268:
265:
257:
252:
249:
215:
212:
178:fractal curves
173:
170:
168:
165:
161:hurst exponent
128:
125:
73:Fractals have
70:
67:
15:
9:
6:
4:
3:
2:
4227:
4216:
4213:
4211:
4208:
4206:
4203:
4201:
4198:
4197:
4195:
4180:
4177:
4175:
4172:
4169:
4168:
4164:
4161:
4160:
4156:
4153:
4152:
4148:
4146:
4143:
4141:
4138:
4134:
4131:
4130:
4128:
4124:
4123:
4121:
4117:
4111:
4108:
4106:
4103:
4101:
4098:
4096:
4093:
4091:
4088:
4086:
4083:
4081:
4078:
4076:
4073:
4071:
4068:
4066:
4063:
4061:
4058:
4056:
4053:
4051:
4048:
4047:
4045:
4041:
4035:
4032:
4030:
4027:
4025:
4022:
4020:
4017:
4013:
4010:
4008:
4007:Brownian tree
4005:
4004:
4003:
4000:
3999:
3997:
3994:
3990:
3984:
3981:
3979:
3976:
3974:
3971:
3970:
3968:
3965:
3961:
3955:
3952:
3950:
3947:
3945:
3942:
3940:
3937:
3935:
3934:Multibrot set
3932:
3928:
3925:
3924:
3923:
3920:
3918:
3915:
3911:
3910:Douady rabbit
3908:
3906:
3903:
3901:
3898:
3897:
3896:
3893:
3891:
3888:
3887:
3885:
3883:
3877:
3869:
3866:
3865:
3864:
3861:
3859:
3856:
3855:
3853:
3851:
3847:
3841:
3838:
3837:
3835:
3833:
3829:
3823:
3820:
3818:
3815:
3813:
3810:
3808:
3805:
3803:
3800:
3798:
3795:
3793:
3790:
3788:
3785:
3781:
3780:Z-order curve
3778:
3776:
3773:
3771:
3768:
3766:
3763:
3761:
3758:
3756:
3753:
3751:
3750:Hilbert curve
3748:
3746:
3743:
3739:
3736:
3735:
3734:
3733:De Rham curve
3731:
3729:
3726:
3725:
3724:
3721:
3719:
3716:
3714:
3711:
3709:
3706:
3704:
3701:
3699:
3698:Menger sponge
3696:
3694:
3691:
3689:
3686:
3684:
3683:Barnsley fern
3681:
3680:
3678:
3676:
3670:
3664:
3661:
3659:
3656:
3652:
3649:
3647:
3644:
3642:
3639:
3637:
3634:
3630:
3627:
3626:
3625:
3622:
3620:
3617:
3616:
3615:
3612:
3611:
3609:
3605:
3601:
3594:
3589:
3587:
3582:
3580:
3575:
3574:
3571:
3565:
3561:
3558:
3555:
3553:
3549:
3546:
3543:
3541:
3538:
3536:
3533:
3532:
3520:
3516:
3512:
3508:
3501:
3493:
3487:
3483:
3476:
3467:
3462:
3458:
3454:
3450:
3446:
3442:
3438:
3431:
3423:
3419:
3415:
3411:
3407:
3403:
3396:
3388:
3384:
3380:
3376:
3369:
3361:
3357:
3353:
3349:
3345:
3341:
3337:
3331:
3323:
3319:
3315:
3311:
3307:
3303:
3299:
3295:
3288:
3274:on 2014-04-13
3270:
3266:
3262:
3258:
3254:
3250:
3246:
3242:
3238:
3231:
3224:
3216:
3212:
3208:
3204:
3200:
3196:
3189:
3181:
3177:
3173:
3169:
3165:
3161:
3157:
3153:
3146:
3138:
3134:
3129:
3124:
3120:
3116:
3112:
3108:
3104:
3100:
3096:
3089:
3081:
3077:
3072:
3067:
3063:
3059:
3054:
3049:
3045:
3041:
3036:
3031:
3027:
3023:
3019:
3012:
3004:
3000:
2996:
2992:
2985:
2977:
2973:
2968:
2963:
2958:
2953:
2949:
2945:
2940:
2935:
2932:(9): e24791.
2931:
2927:
2923:
2916:
2914:
2905:
2899:
2892:
2891:
2883:
2875:
2871:
2867:
2863:
2859:
2855:
2851:
2847:
2843:
2839:
2835:
2831:
2824:
2816:
2812:
2808:
2804:
2800:
2796:
2789:
2775:on 2021-10-19
2774:
2770:
2766:
2762:
2758:
2754:
2750:
2746:
2742:
2738:
2734:
2730:
2723:
2708:
2702:
2698:
2697:
2689:
2681:
2677:
2672:
2667:
2663:
2659:
2655:
2651:
2647:
2643:
2639:
2632:
2624:
2620:
2615:
2610:
2605:
2600:
2596:
2592:
2588:
2581:
2573:
2569:
2564:
2559:
2554:
2549:
2545:
2541:
2537:
2530:
2528:
2519:
2515:
2511:
2507:
2502:
2497:
2493:
2489:
2482:
2474:
2470:
2465:
2460:
2456:
2452:
2447:
2442:
2438:
2434:
2430:
2423:
2415:
2411:
2406:
2401:
2397:
2393:
2389:
2385:
2381:
2374:
2360:on 2007-10-12
2359:
2355:
2349:
2335:
2331:
2327:
2323:
2320:(1): 99–103.
2319:
2315:
2311:
2304:
2296:
2292:
2288:
2284:
2280:
2276:
2269:
2261:
2257:
2252:
2247:
2243:
2239:
2235:
2228:
2220:
2216:
2212:
2208:
2204:
2200:
2192:
2184:
2180:
2175:
2170:
2166:
2162:
2158:
2154:
2150:
2146:
2142:
2135:
2133:
2124:
2120:
2116:
2112:
2108:
2104:
2096:
2094:
2085:
2081:
2076:
2071:
2068:(1): 95–119.
2067:
2063:
2059:
2052:
2050:
2041:
2037:
2033:
2029:
2025:
2021:
2014:
2006:
2002:
1998:
1994:
1990:
1986:
1982:
1978:
1974:
1970:
1963:
1955:
1951:
1946:
1941:
1937:
1933:
1928:
1923:
1919:
1915:
1911:
1907:
1903:
1896:
1888:
1884:
1880:
1876:
1869:
1861:
1857:
1852:
1847:
1843:
1839:
1834:
1829:
1825:
1821:
1817:
1813:
1809:
1802:
1794:
1790:
1785:
1780:
1776:
1772:
1768:
1764:
1760:
1756:
1752:
1748:
1744:
1737:
1729:
1725:
1721:
1717:
1713:
1709:
1705:
1701:
1694:
1686:
1682:
1678:
1674:
1670:
1666:
1659:
1651:
1647:
1643:
1639:
1635:
1631:
1624:
1616:
1612:
1608:
1604:
1600:
1596:
1592:
1588:
1584:
1580:
1573:
1565:
1561:
1557:
1553:
1549:
1545:
1541:
1537:
1533:
1526:
1518:
1514:
1509:
1504:
1500:
1496:
1491:
1486:
1482:
1478:
1474:
1470:
1466:
1459:
1451:
1447:
1443:
1439:
1435:
1431:
1427:
1423:
1416:
1408:
1404:
1400:
1396:
1392:
1388:
1384:
1380:
1373:
1365:
1361:
1356:
1351:
1347:
1343:
1339:
1335:
1331:
1324:
1316:
1312:
1308:
1304:
1296:
1294:
1292:
1283:
1279:
1274:
1269:
1265:
1261:
1257:
1250:
1242:
1238:
1234:
1230:
1226:
1222:
1215:
1208:
1206:9783642708824
1202:
1198:
1194:
1190:
1183:
1175:
1171:
1166:
1161:
1157:
1153:
1149:
1145:
1141:
1137:
1133:
1129:
1125:
1118:
1116:
1100:
1096:
1090:
1082:
1078:
1074:
1070:
1066:
1062:
1058:
1054:
1047:
1045:
1030:on 2021-10-19
1029:
1025:
1021:
1017:
1013:
1009:
1005:
1001:
997:
993:
989:
985:
981:
977:
970:
968:
966:
957:
953:
949:
943:
939:
938:10.1142/12988
935:
931:
930:
922:
920:
904:
898:
895:. Macmillan.
894:
893:
885:
883:
881:
879:
877:
875:
866:
862:
858:
854:
848:
842:
836:
828:
824:
820:
816:
812:
806:
802:
798:
794:
787:
779:
775:
770:
765:
760:
755:
751:
747:
743:
739:
735:
728:
720:
716:
711:
706:
702:
698:
694:
690:
686:
679:
670:
665:
661:
657:
653:
646:
638:
634:
630:
626:
619:
611:
605:
601:
594:
592:
583:
581:9780849327827
577:
573:
569:
566:. CRC Press.
565:
558:
556:
554:
552:
543:
539:
535:
531:
527:
523:
519:
515:
511:
507:
503:
496:
494:
489:
480:
477:
475:
472:
470:
467:
466:
458:
455:
454:
448:
442:
438:
435:
433:
430:
428:
424:
422:
419:
416:
413:
411:
407:
405:
401:
397:
394:, especially
393:
390:
389:
388:
384:
381:
379:
376:
374:
371:
369:
366:
364:
361:
359:
356:
354:
351:
349:
346:
343:
342:
341:
339:
335:
331:
328:
326:
323:
321:
318:
316:
313:
310:
306:
304:
301:
298:
294:
291:
289:
285:
281:
278:
275:
272:
269:
266:
263:
262:
261:
260:
256:
248:
246:
241:
236:
234:
228:
226:
221:
211:
209:
204:
200:
195:
191:
187:
183:
179:
164:
162:
158:
154:
150:
146:
142:
138:
134:
124:
123:
122:
116:
114:
110:
109:
108:self-affinity
104:
103:
98:
97:
92:
88:
84:
80:
76:
66:
64:
60:
56:
52:
48:
43:
39:
35:
32:is assessing
31:
23:
19:
4200:Chaos theory
4179:Chaos theory
4174:Kaleidoscope
4165:
4157:
4149:
4075:Gaston Julia
4055:Georg Cantor
3880:Escape-time
3812:Gosper curve
3760:Lévy C curve
3745:Dragon curve
3624:Box-counting
3510:
3506:
3500:
3481:
3475:
3440:
3436:
3430:
3405:
3401:
3395:
3378:
3374:
3368:
3343:
3339:
3330:
3297:
3293:
3287:
3276:. Retrieved
3269:the original
3240:
3236:
3223:
3198:
3194:
3188:
3158:(1): 27–33.
3155:
3151:
3145:
3102:
3098:
3088:
3025:
3021:
3011:
2994:
2990:
2984:
2929:
2925:
2889:
2882:
2833:
2829:
2823:
2798:
2794:
2788:
2777:. Retrieved
2773:the original
2736:
2732:
2722:
2710:. Retrieved
2699:. Springer.
2695:
2688:
2648:(1): 22964.
2645:
2641:
2631:
2594:
2590:
2580:
2543:
2539:
2491:
2487:
2481:
2436:
2432:
2422:
2387:
2383:
2373:
2362:. Retrieved
2358:the original
2348:
2337:. Retrieved
2317:
2313:
2303:
2278:
2274:
2268:
2241:
2237:
2227:
2202:
2198:
2191:
2148:
2144:
2106:
2102:
2065:
2061:
2023:
2019:
2013:
1972:
1968:
1962:
1909:
1905:
1895:
1878:
1874:
1868:
1815:
1811:
1801:
1750:
1746:
1736:
1703:
1699:
1693:
1668:
1664:
1658:
1633:
1629:
1623:
1582:
1578:
1572:
1539:
1535:
1525:
1472:
1468:
1458:
1425:
1421:
1415:
1382:
1378:
1372:
1337:
1333:
1323:
1306:
1302:
1263:
1259:
1249:
1224:
1220:
1214:
1188:
1182:
1131:
1127:
1103:. Retrieved
1089:
1059:(1): 23–26.
1056:
1052:
1032:. Retrieved
1028:the original
983:
979:
928:
906:. Retrieved
891:
856:
847:
835:
792:
786:
741:
737:
727:
692:
688:
678:
659:
655:
645:
628:
624:
618:
599:
563:
509:
505:
469:Multifractal
446:
383:Soil studies
348:Neuroscience
344:Urban growth
254:
237:
233:conservation
229:
217:
184:calculated;
175:
167:Applications
133:box counting
130:
118:
117:
106:
100:
94:
72:
51:data science
29:
28:
18:
4170:(1987 book)
4162:(1986 book)
4154:(1982 book)
4140:Fractal art
4060:Bill Gosper
4024:Lévy flight
3770:Peano curve
3765:Moore curve
3651:Topological
3636:Correlation
3513:: 161–170.
3466:2158/257208
2494:: 612–619.
2205:: 118–127.
1542:(5): 1239.
1340:: 169–171.
1134:(1): 1884.
631:: 155–179.
373:Archaeology
153:fractal art
91:statistical
4194:Categories
3978:Orbit trap
3973:Buddhabrot
3966:techniques
3954:Mandelbulb
3755:Koch curve
3688:Cantor set
3300:(1): 1–8.
3278:2014-04-10
3035:1806.03889
2779:2020-12-21
2712:1 February
2501:1702.03912
2364:2007-10-21
2339:2019-03-27
1753:(1): 315.
1379:Biosystems
1105:2012-02-08
1097:. ImageJ.
1034:2020-12-21
908:1 February
485:References
378:Seismology
299:complexity
286:slides in
199:ecosystems
194:ecological
79:complexity
4085:Paul Lévy
3964:Rendering
3949:Mandelbox
3895:Julia set
3807:Hexaflake
3738:Minkowski
3658:Recursion
3641:Hausdorff
3408:: 37–78.
3360:118918429
3062:1664-042X
2939:1104.4682
2858:0031-9007
2815:136564926
2455:1662-5161
2334:146350786
2260:1045-2249
2219:0022-0981
2165:1742-5689
2109:: 44–53.
2084:1880-2117
1997:1751-8113
1936:0027-8424
1842:0027-8424
1775:2045-2322
1720:1461-023X
1650:0967-0637
1607:0028-0836
1564:0361-5995
1499:0027-8424
1399:0303-2647
1364:0171-8630
1282:0142-7873
1156:2045-2322
1008:0036-8075
956:248575991
865:1793-6543
542:234272453
534:0218-348X
368:Geography
358:Pathology
297:Coastline
220:behaviour
208:criticism
4215:Fractals
3995:fractals
3882:fractals
3850:L-system
3792:T-square
3600:Fractals
3560:Archived
3548:Archived
3387:16393505
3322:40311727
3314:21118245
3265:14784161
3257:18595800
3180:12268410
3172:18495248
3137:14645092
3080:30618789
3028:: 1767.
2991:Fractals
2976:21949753
2926:PLOS ONE
2874:16203048
2866:18518581
2769:15662830
2761:17837158
2680:34824290
2623:19594934
2572:19668394
2518:18259316
2473:28184193
2414:19528254
2295:53184132
2183:21429908
2123:53475196
2005:13887492
1954:22529349
1860:14566048
1793:22419991
1517:19363160
1174:23703258
1099:Archived
1081:17022186
1073:11755014
1024:15662830
1016:17837158
827:22136019
819:19163560
778:24967904
738:PLOS ONE
719:19528254
506:Fractals
463:See also
288:medicine
3944:Tricorn
3797:n-flake
3646:Packing
3629:Higuchi
3619:Assouad
3445:Bibcode
3422:7481018
3215:2716356
3128:1303704
3107:Bibcode
3071:6295567
3040:Bibcode
2967:3176775
2944:Bibcode
2838:Bibcode
2741:Bibcode
2733:Science
2671:8616909
2650:Bibcode
2614:2716356
2597:: 130.
2563:2698675
2464:5266716
2405:2746620
2174:3163426
2028:Bibcode
1977:Bibcode
1945:3358854
1914:Bibcode
1820:Bibcode
1784:3303145
1755:Bibcode
1728:6059069
1673:Bibcode
1615:4362382
1587:Bibcode
1544:Bibcode
1508:2678466
1477:Bibcode
1450:3140271
1442:9082983
1422:Science
1407:7165795
1342:Bibcode
1241:3235975
1165:3662970
1136:Bibcode
988:Bibcode
980:Science
769:4072666
746:Bibcode
710:2746620
662:: 1–8.
514:Bibcode
400:organic
363:Geology
186:natural
87:integer
55:science
34:fractal
4043:People
3993:Random
3900:Filled
3868:H tree
3787:String
3675:system
3488:
3420:
3385:
3358:
3320:
3312:
3263:
3255:
3213:
3178:
3170:
3135:
3125:
3078:
3068:
3060:
2974:
2964:
2900:
2872:
2864:
2856:
2813:
2767:
2759:
2703:
2678:
2668:
2621:
2611:
2570:
2560:
2516:
2471:
2461:
2453:
2439:: 14.
2412:
2402:
2332:
2293:
2258:
2217:
2181:
2171:
2163:
2121:
2082:
2003:
1995:
1952:
1942:
1934:
1858:
1851:240693
1848:
1840:
1791:
1781:
1773:
1726:
1718:
1648:
1613:
1605:
1579:Nature
1562:
1515:
1505:
1497:
1448:
1440:
1405:
1397:
1362:
1280:
1239:
1203:
1172:
1162:
1154:
1079:
1071:
1022:
1014:
1006:
954:
944:
899:
863:
825:
817:
807:
776:
766:
717:
707:
606:
578:
540:
532:
447:
427:MARPAT
330:Signal
4119:Other
3418:S2CID
3356:S2CID
3318:S2CID
3272:(PDF)
3261:S2CID
3233:(PDF)
3176:S2CID
3030:arXiv
2934:arXiv
2894:(PDF)
2870:S2CID
2811:S2CID
2765:S2CID
2514:S2CID
2496:arXiv
2330:S2CID
2291:S2CID
2119:S2CID
2001:S2CID
1724:S2CID
1611:S2CID
1446:S2CID
1237:JSTOR
1077:S2CID
1020:S2CID
952:S2CID
823:S2CID
538:S2CID
203:xylem
83:scale
3486:ISBN
3383:PMID
3310:PMID
3253:PMID
3211:PMID
3168:PMID
3133:PMID
3076:PMID
3058:ISSN
2972:PMID
2898:ISBN
2862:PMID
2854:ISSN
2757:PMID
2714:2012
2701:ISBN
2676:PMID
2619:PMID
2568:PMID
2469:PMID
2451:ISSN
2410:PMID
2256:ISSN
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