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TO DRAW OR NOT TO DRAW: UNDERSTANDING THE TEMPORAL ORGANIZATION OF DRAWING BEHAVIOR USING FRACTAL ANALYSES

Université de Strasbourg, CNRS, IPHC UMR 7178, 67000 Strasbourg, France

Current Address: Institut Pluridisciplinaire Hubert Curien, Département Écologie, Physiologie et Éthologie, 23, rue Becquerel, 67087 Strasbourg, France.

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ANDREW J. J. MACINTOSH

Kyoto University, Wildlife Research Center, Inuyama Campus, Inuyama, Japan

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XAVIER MEYER

Université de Strasbourg, CNRS, IPHC UMR 7178, 67000 Strasbourg, France

Kyoto University, Wildlife Research Center, Inuyama Campus, Inuyama, Japan

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JÉRÔME HOSSELET

Université de Strasbourg, CNRS, IPHC UMR 7178, 67000 Strasbourg, France

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MARIE PELÉ

ANTHROPO-LAB, ETHICS EA 7446, Université Catholique de Lille, F-59000 Lille, France

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, and

CÉDRIC SUEUR

Université de Strasbourg, CNRS, IPHC UMR 7178, 67000 Strasbourg, France

Institut Universitaire de France, Paris, France

E-mail Address: [email protected]

Corresponding author.

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https://doi.org/10.1142/S0218348X23500093Cited by:0 (Source: Crossref)

Abstract

Studies on drawing often focused on spatial aspects of the finished products. Here, the drawing behavior was studied by analyzing its intermittent process, between drawing (i.e. marking a surface) and interruption (i.e. a pause in the marking gesture). To assess how this intermittence develops with age, we collected finger-drawings on a touchscreen by 185 individuals (children and adults). We measured the temporal structure of each drawing sequence to determine its complexity. To do this, we applied temporal fractal estimators to each drawing time series before combining them in a Principal Component Analysis procedure. The youngest children (3-year-old) drew in a more stereotypical way with long-range dependence detected in their alternations between states. Among older children and adults, the complexity of drawing sequences increased showing a less predictable behavior as their drawings become more detailed and figurative. This study improves our understanding of the temporal aspects of drawing behavior, and contributes to an objective understanding of its ontogeny.

Keywords:

References

1. N. H. Freeman, Drawing: Public instruments of representation, in Systems of Representation in Children, eds. C. Pratt and A. F. Garton (Wiley, Chichester, UK, 1993), pp. 113–132 Google Scholar
2. L. Martinet, C. Sueur, S. Hirata, J. Hosselet, T. Matsuzawa and M. Pelé, New indices to characterize drawing behavior in humans (Homo sapiens) and chimpanzees (Pan troglodytes), Sci. Rep. 11 (2021) 3860, https://doi.org/10.1038/s41598-021-83043-0. Crossref, Web of Science, Google Scholar
3. G. H. Luquet, Le dessin enfantin (Bibliothèque de psychologie de l’enfant et de pédagogie) (Delachaux & Niestl, 1927). Google Scholar
4. J. Willats, Making Sense of Children’s Drawings (Psychology Press, 2005). Google Scholar
5. E. Adi-Japha, I. Levin and S. Solomon, Emergence of representation in drawing: The relation between kinematic and referential aspects, Cogn. Dev. 13 (1998) 25–51. Crossref, Web of Science, Google Scholar
6. I. D. Cherney, C. S. Seiwert, T. M. Dickey and J. D. Flichtbeil, Children’s Drawings: A mirror to their minds, Educ. Psychol. 26 (2006) 127–142, https://doi.org/10.1080/01443410500344167. Crossref, Google Scholar
7. L. Wright and F. Black, Monochrome males and colorful females: Do gender and age influence the color and content of drawings? SAGE Open 3 (2013) 215824401350925, https://doi.org/10.1177/2158244013509254. Crossref, Google Scholar
8. R. P. Jolley, E. L. Knox and S. G. Foster, The relationship between children’s production and comprehension of realism in drawing, British J. Develop. Psychol. 18(4) (2000) 557–582. Crossref, Google Scholar
9. S. M. Turgeon, Sex differences in children’s free drawings and their relationship to 2D:4D ratio, Personal Individ. Differ. 45 (2008) 527–532. Crossref, Web of Science, Google Scholar
10. E. Adi-Japha, I. Levin and S. Solomon, Emergence of representation in drawing: The relation between kinematic and referential aspects, Cogn. Dev. 13 (1998) 25–51. Crossref, Web of Science, Google Scholar
11. B. B. Mandelbrot Fractals: Form, Chance and Dimension, 1st edn. (W. H. Freeman & Company, 1977). Google Scholar
12. A. Rinaldo, I. Rodriguez-Iturbe, R. Rigon, E. Ijjasz-Vasquez and R. L. Bras, Self-organized fractal river networks, Phys. Rev. Lett. 70 (1993) 822. Crossref, Web of Science, Google Scholar
13. T. R. Nelson, B. J. West and A. L. Goldberger, The fractal lung: Universal and species-related scaling patterns, Experientia 46 (1990) 251–254. Crossref, Google Scholar
14. C.-K. Peng et al., Quantifying fractal dynamics of human respiration: Age and gender effects, Ann. Biomed. Eng. 30 (2002) 683–692. Crossref, Web of Science, Google Scholar
15. B. Weiss, Z. Clemens, R. Bódizs, Z. Vágó and P. Halász, Spatio-temporal analysis of monofractal and multifractal properties of the human sleep EEG, J. Neurosci. Methods 185 (2009) 116–124, https://doi.org/10.1016/j.jneumeth.2009.07.027. Crossref, Web of Science, Google Scholar
16. A. J. MacIntosh, The fractal primate: Interdisciplinary science and the math behind the monkey, Primate Res. 30 (2014) 95–119. Crossref, Google Scholar
17. K. M. D. Rutherford, M. J. Haskell, C. Glasbey, R. B. Jones and A. B. Lawrence, Detrended fluctuation analysis of behavioural responses to mild acute stressors in domestic hens, Appl. Anim. Behav. Sci. 83 (2003) 125–139, https://doi.org/10.1016/S0168-1591(03)00115-1. Crossref, Web of Science, Google Scholar
18. C. Sueur, A non-lévy random walk in chacma baboons: What does it mean? PLoS One 6 (2011) e16131, https://doi.org/10.1371/journal.pone.0016131. Crossref, Web of Science, Google Scholar
19. C. Sueur, L. Briard and O. Petit, Individual analyses of lévy walk in semi-free ranging tonkean macaques (Macaca tonkeana), PLoS One 6 (2011) e26788, https://doi.org/10.1371/journal.pone.0026788. Crossref, Web of Science, Google Scholar
20. R. Taylor, B. Spehar, C. Hagerhall and P. Van Donkelaar, Perceptual and physiological responses to Jackson Pollock’s fractals, Front. Hum. Neurosci. 5 (2011) 60. Crossref, Google Scholar
21. C. A. Marlow, I. V. Viskontas, A. Matlin, C. Boydston, A. Boxer and R. P. Taylor, Temporal structure of human gaze dynamics is invariant during free viewing, PLoS One 10 (2015) e0139379, https://doi.org/10.1371/journal.pone.0139379. Crossref, Web of Science, Google Scholar
22. P. Moon et al., Fractal images induce fractal pupil dilations and constrictions, Int. J. Psychophysiol. 93 (2014) 316–321, https://doi.org/10.1016/j.ijpsycho.2014.06.013. Crossref, Web of Science, Google Scholar
23. D. W. Sims et al., Scaling laws of marine predator search behaviour, Nature 451 (2008) 1098–1102, https://doi.org/10.1038/nature06518. Crossref, Web of Science, Google Scholar
24. G. M. Viswanathan, S. V. Buldyrev, S. Havlin, M. G. E. da Luz, E. P. Raposo and H. E. Stanley, Optimizing the success of random searches, Nature 401 (1999) 911–914, https://doi.org/10.1038/44831. Crossref, Web of Science, Google Scholar
25. C. L. Alados et al., Fractal structure of sequential behaviour patterns: an indicator of stress, Anim Behav 51 (1996) 437–443. Crossref, Web of Science, Google Scholar
26. D. Delignières, K. Torre and L. Lemoine, Methodological issues in the application of monofractal analyses in psychological and behavioral research, Nonlinear Dyn. Psychol. Life Sci. 9 (2005) 435–461. Google Scholar
27. MacIntosh , C. L. Alados and M. A. Huffman, Fractal analysis of behaviour in a wild primate: Behavioural complexity in health and disease, J. R. Soc. Interf. 8 (2011) 1497–1509, https://doi.org/10.1098/rsif.2011.0049. Crossref, Web of Science, Google Scholar
28. G. A. Marıa, J. Escós and C. L. Alados, Complexity of behavioural sequences and their relation to stress conditions in chickens (Gallus gallus domesticus): A non-invasive technique to evaluate animal welfare, Appl. Anim. Behav. Sci. 86 (2004) 93–104. Crossref, Web of Science, Google Scholar
29. X. Meyer et al., Oceanic thermal structure mediates dive sequences in a foraging seabird, Ecol. Evol. 10 (2020) 6610–6622. Crossref, Web of Science, Google Scholar
30. A. Paraschiv-Ionescu, E. Buchser, B. Rutschmann and K. Aminian, Nonlinear analysis of human physical activity patterns in health and disease, Phys. Rev. E 77 (2008) 021913, https://doi.org/10.1103/PhysRevE.77.021913. Crossref, Web of Science, Google Scholar
31. D. Rybski, S. V. Buldyrev, S. Havlin, F. Liljeros and H. A. Makse, Scaling laws of human interaction activity, Proc. Natl. Acad. Sci. 106 (2009) 12640–12645, https://doi.org/10.1073/pnas.0902667106. Crossref, Google Scholar
32. D. N. Fernandes and T. Chau, Fractal dimensions of pacing and grip force in drawing and handwriting production, J. Biomech. 41 (2008) 40–46, https://doi.org/10.1016/j.jbiomech.2007.07.017. Crossref, Web of Science, Google Scholar
33. T. Stadnitski, Measuring fractality, Front. Physiol. 3 (2012) 127. Crossref, Web of Science, Google Scholar
34. E. Stroe-Kunold, T. Stadnytska, J. Werner and S. Braun, Estimating long-range dependence in time series: An evaluation of estimators implemented in R, Behav. Res. Methods 41 (2009) 909–923. Crossref, Web of Science, Google Scholar
35. M. Tanaka, M. Tomonaga and T. Matsuzawa, Finger drawing by infant chimpanzees (Pan troglodytes), Anim. Cogn. 6 (2003) 245–251, https://doi.org/10.1007/s10071-003-0198-3. Crossref, Web of Science, Google Scholar
36. M. G. Longstaff and R. A. Heath, A nonlinear analysis of the temporal characteristics of handwriting, Human Mov. Sci. 18 (1999) 485–524, https://doi.org/10.1016/S0167-9457(99)00028-7. Crossref, Web of Science, Google Scholar
37. T. Stadnytska, S. Braun and J. Werner, Analyzing fractal dynamics employing R, Nonlinear Dynam. Psychol. Life Sci. 14 (2010) 117–144. Web of Science, Google Scholar
38. T. Karagiannis, M. Molle and M. Faloutsos, Understanding the limitations of estimation methods for long-range dependence, Technical Report, University of California, Riverside, TR UCR-CS-2006-10245 (2006). Google Scholar
39. M. J. Cannon, D. B. Percival, D. C. Caccia, G. M. Raymond and J. B. Bassingthwaighte, Evaluating scaled windowed variance methods for estimating the Hurst coefficient of time series, Phys. Stat. Mech. Appl. 241 (1997) 606–626, https://doi.org/10.1016/S0378-4371(97)00252-5. Crossref, Google Scholar
40. B. B. Mandelbrot and J. W. Van Ness, Fractional Brownian motions, fractional noises and applications, SIAM Rev. 10 (1968) 422–437. Crossref, Web of Science, Google Scholar
41. A. Eke, P. Herman, L. Kocsis and L. R. Kozak, Fractal characterization of complexity in temporal physiological signals, Physiol. Meas. 23(1) (2002) R1–38. Crossref, Web of Science, Google Scholar
42. A. K. Kalashyan, M. Buiatti and P. Grigolini, Ergodicity breakdown and scaling from single sequences, Chaos Solitons Fractals 39 (2009) 895–909, https://doi.org/10.1016/j.chaos.2007.01.062. Crossref, Web of Science, Google Scholar
43. C.-K. Peng, S. Havlin, H. E. Stanley and A. L. Goldberger, Quantification of scaling exponents and crossover phenomena in nonstationary heartbeat time series, Chaos Interdiscip. J. Nonlinear Sci. 5 (1995) 82–87. Crossref, Web of Science, Google Scholar
44. A. J. J. MacIntosh, L. Pelletier, A. Chiaradia, A. Kato and Y. Ropert-Coudert, Temporal fractals in seabird foraging behaviour: Diving through the scales of time, Sci. Rep. 3 (2013) 1884. Crossref, Web of Science, Google Scholar
45. X. Meyer et al., Shallow divers, deep waters and the rise of behavioural stochasticity, Marine Biol. 164 (2017), https://doi.org/10.1007/s00227-017-3177-y. Crossref, Web of Science, Google Scholar
46. W. Constantine and D. Percival, The fractal Package (2007). Google Scholar
47. L. Seuront Fractals and Multifractals in Ecology and Aquatic Science (CRC Press, 2009). Crossref, Google Scholar
48. S. Mercik, K. Weron, K. Burnecki and A. Weron, Enigma of self-similarity of fractional Levy stable motions, Acta Phys. Pol. B 34 (2003) 3773. Web of Science, Google Scholar
49. D. Delignieres, S. Ramdani, S. Lemoine, K. Torre, M. Fortes and G. Ninot, Fractal analyses for ‘short’time series: A re-assessment of classical methods, J. Math. Psychol. 50 (2006) 525–544. Crossref, Web of Science, Google Scholar
50. A. Eke et al., Physiological time series: distinguishing fractal noises from motions, Pflüg Arch., Eur. J. Physiol. 439 (2000) 403–415, https://doi.org/10.1007/s004249900135. Crossref, Web of Science, Google Scholar
51. J. Huang, somebm: Some Brownian motions simulation functions (2013), http://CRAN. R-project. org/package= somebm. Google Scholar
52. A. Berni et al., Effect of vascular risk factors on increase in carotid and femoral intima-media thickness. Identification of a risk scale, Atherosclerosis 216 (2011) 109–114. Crossref, Web of Science, Google Scholar
53. J. Pinheiro, D. Bates, S. DebRoy and D. Sarkar, Team RC. nlme: Linear and nonlinear mixed effects models, R Package Version 3 (2006) 109. Google Scholar
54. K. Barton, MuMIn: multi-model inference. Httpr-Forge R-Proj Orgprojectsmumin (2009). Google Scholar
55. N. Cohn, Explaining ‘I can’t draw’: Parallels between the structure and development of language and drawing, Human Develop. 55 (2012) 167–192. Crossref, Web of Science, Google Scholar
56. F. Bartumeus, Behavioral intermittence, Lévy patterns, and randomness in animal movement, Oikos 118 (2009) 488–494, https://doi.org/10.1111/j.1600-0706.2009.17313.x. Crossref, Web of Science, Google Scholar
57. T. Albers and G. Radons, Nonergodicity of d-dimensional generalized Levy walks and their relation to other space-time coupled models, Phys. Rev. E 105 (2022) 014113, https://doi.org/10.1103/PhysRevE.105.014113. Crossref, Web of Science, Google Scholar
58. A. J. J. MacIntosh, C. L. Alados and M. A. Huffman, Fractal analysis of behaviour in a wild primate: Behavioural complexity in health and disease, J. R. Soc. Interf. 8 (2011) 1497–1509, https://doi.org/10.1098/rsif.2011.0049. Crossref, Web of Science, Google Scholar
59. G. M. Viswanathan, V. Afanasyev, S. V. Buldyrev, E. J. Murphy, P. A. Prince and H. E. Stanley, Lévy flight search patterns of wandering albatrosses, Nature 381 (1996) 413–415. Crossref, Web of Science, Google Scholar
60. S. J. Simpson, R. M. Sibly, K. P. Lee, S. T. Behmer and D. Raubenheimer, Optimal foraging when regulating intake of multiple nutrients, Anim. Behav. 68 (2004) 1299–1311, https://doi.org/10.1016/j.anbehav.2004.03.003. Crossref, Web of Science, Google Scholar
61. R. P. Taylor, The potential of biophilic fractal designs to promote health and performance: A review of experiments and applications, Sustainability 13 (2021) 823, https://doi.org/10.3390/su13020823. Crossref, Web of Science, Google Scholar
62. J. Billington, R. J. Webster, T. N. Sherratt, R. M. Wilkie and C. Hassall, The (Under)Use of Eye-Tracking in Evolutionary Ecology, Trends Ecol. Evol. 35 (2020) 495–502, https://doi.org/10.1016/j.tree.2020.01.003. Crossref, Web of Science, Google Scholar
63. K. E. Robles et al., Aesthetics and psychological effects of fractal based design, Front Psychol. 12 (2021). Crossref, Web of Science, Google Scholar
64. D. D. Huntsman and G. Bulaj, Healthy dwelling: design of biophilic interior environments fostering self-care practices for people living with migraines, chronic pain, and depression, Int. J. Environ. Res. Public Health 19 (2022) 2248, https://doi.org/10.3390/ijerph19042248. Crossref, Web of Science, Google Scholar
65. V. Marmelat, K. Torre and D. Delignieres, Relative roughness: An index for testing the suitability of the monofractal model, Front. Physiol. 3(208) (2012), https://doi.org/10.3389/fphys.2012.00208. Google Scholar