{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,5,6]],"date-time":"2026-05-06T06:55:55Z","timestamp":1778050555352,"version":"3.51.4"},"reference-count":52,"publisher":"MDPI AG","issue":"8","license":[{"start":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T00:00:00Z","timestamp":1691712000000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/creativecommons.org\/licenses\/by\/4.0\/"}],"funder":[{"name":"President and Board of Trustees of Loyola University Chicago"}],"content-domain":{"domain":[],"crossmark-restriction":false},"short-container-title":["Symmetry"],"abstract":"<jats:p>Little is known about the detection of and preference for multiple simultaneous parallel axes of symmetry. Neuroscientists have suggested that the detection of symmetry occurs in extrastriate brain areas with large receptive fields. Such large receptive fields may potentially hinder the simultaneous detection of more than one axis of symmetry. In contrast, psychophysicists have found that symmetry detection occurs within small spatial windows, allowing for the concurrent detection of multiple axes of symmetry. Using psychophysical and computational methods, we aim to test whether multiple axes of symmetry can be detected in parallel and to understand the role of multiple axes of symmetry on aesthetic valence. Experiment 1 provides evidence that multiple axes of symmetry cannot be detected simultaneously. However, with relatively long temporal integration, people can detect them. Experiment 2 suggests that multiple axes of symmetry tend to increase preference. However, the preference for symmetry is not universal because, although most people prefer symmetry, others prefer complex images without axes of symmetry. We present and test a computational model that explains the results of these experiments.<\/jats:p>","DOI":"10.3390\/sym15081568","type":"journal-article","created":{"date-parts":[[2023,8,11]],"date-time":"2023-08-11T10:20:16Z","timestamp":1691749216000},"page":"1568","update-policy":"https:\/\/doi.org\/10.3390\/mdpi_crossmark_policy","source":"Crossref","is-referenced-by-count":10,"title":["Multiple Axes of Visual Symmetry: Detection and Aesthetic Preference"],"prefix":"10.3390","volume":"15","author":[{"given":"Maria","family":"Pombo","sequence":"first","affiliation":[{"name":"Graduate School of Arts and Sciences, Georgetown University, Washington, DC 20057, USA"},{"name":"Department of Psychology, New York University, New York, NY 10003, USA"}]},{"given":"Hassan","family":"Aleem","sequence":"additional","affiliation":[{"name":"Graduate School of Arts and Sciences, Georgetown University, Washington, DC 20057, USA"},{"name":"Interdisciplinary Program in Neuroscience, Georgetown University, Washington, DC 20057, USA"},{"name":"Department of Molecular Pharmacology and Neuroscience, Loyola University Chicago, Chicago, IL 60153, USA"}]},{"given":"Norberto M.","family":"Grzywacz","sequence":"additional","affiliation":[{"name":"Graduate School of Arts and Sciences, Georgetown University, Washington, DC 20057, USA"},{"name":"Interdisciplinary Program in Neuroscience, Georgetown University, Washington, DC 20057, USA"},{"name":"Department of Molecular Pharmacology and Neuroscience, Loyola University Chicago, Chicago, IL 60153, USA"},{"name":"Department of Psychology, Loyola University Chicago, Chicago, IL 60660, USA"}]}],"member":"1968","published-online":{"date-parts":[[2023,8,11]]},"reference":[{"key":"ref_1","first-page":"374","article-title":"Symmetry Is in the Eye of the \u2018Beeholder\u2019: Innate Preference for Bilateral Symmetry in Flower-Na\u00efve Bumblebees","volume":"91","author":"Gumbert","year":"2004","journal-title":"Naturwissenschaften"},{"key":"ref_2","doi-asserted-by":"crossref","first-page":"1510","DOI":"10.3390\/sym2031510","article-title":"Behind the Looking-Glass: A Review on Human Symmetry Perception","volume":"2","author":"Treder","year":"2010","journal-title":"Symmetry"},{"key":"ref_3","doi-asserted-by":"crossref","first-page":"221","DOI":"10.1068\/p230221","article-title":"The Salience of Vertical Symmetry","volume":"23","author":"Wenderoth","year":"1994","journal-title":"Perception"},{"key":"ref_4","doi-asserted-by":"crossref","first-page":"77","DOI":"10.1146\/annurev-psych-120710-100504","article-title":"Visual Aesthetics and Human Preference","volume":"64","author":"Palmer","year":"2013","journal-title":"Annu. Rev. Psychol."},{"key":"ref_5","doi-asserted-by":"crossref","first-page":"241","DOI":"10.1016\/j.actpsy.2009.01.001","article-title":"Just How Stable Are Stable Aesthetic Features? Symmetry, Complexity, and the Jaws of Massive Familiarization","volume":"130","author":"Tinio","year":"2009","journal-title":"Acta Psychol."},{"key":"ref_6","doi-asserted-by":"crossref","first-page":"109","DOI":"10.2307\/1576340","article-title":"Symmetry as a Superprinciple of Science and Art","volume":"29","author":"Voloshinov","year":"1996","journal-title":"Leonardo"},{"key":"ref_7","doi-asserted-by":"crossref","first-page":"94","DOI":"10.3389\/fnhum.2017.00094","article-title":"Inferring Master Painters\u2019 Esthetic Biases from the Statistics of Portraits","volume":"11","author":"Aleem","year":"2017","journal-title":"Front. Hum. Neurosci."},{"key":"ref_8","doi-asserted-by":"crossref","first-page":"1305","DOI":"10.1068\/p5794","article-title":"Goodness of Regularity in Dot Patterns: Global Symmetry, Local Symmetry, and Their Interactions","volume":"36","author":"Nucci","year":"2007","journal-title":"Perception"},{"key":"ref_9","doi-asserted-by":"crossref","first-page":"529","DOI":"10.1126\/science.1109676","article-title":"Parallel and Serial Neural Mechanisms for Visual Search in Macaque Area V4","volume":"308","author":"Bichot","year":"2005","journal-title":"Science"},{"key":"ref_10","doi-asserted-by":"crossref","first-page":"223","DOI":"10.1016\/j.tics.2004.03.004","article-title":"The Brain Circuitry of Attention","volume":"8","author":"Shipp","year":"2004","journal-title":"Trends Cogn. Sci."},{"key":"ref_11","doi-asserted-by":"crossref","first-page":"7585","DOI":"10.1523\/JNEUROSCI.0948-08.2008","article-title":"Brain Mechanisms of Serial and Parallel Processing during Dual-Task Performance","volume":"28","author":"Sigman","year":"2008","journal-title":"J. Neurosci."},{"key":"ref_12","doi-asserted-by":"crossref","first-page":"413","DOI":"10.3758\/BF03205058","article-title":"Detection of Symmetry in Tachistoscopically Presented Dot Patterns: Effects of Multiple Axes and Skewing","volume":"50","author":"Wagemans","year":"1991","journal-title":"Percept. Psychophys."},{"key":"ref_13","doi-asserted-by":"crossref","first-page":"3159","DOI":"10.1073\/pnas.0500319102","article-title":"Symmetry Activates Extrastriate Visual Cortex in Human and Nonhuman Primates","volume":"102","author":"Sasaki","year":"2005","journal-title":"Proc. Natl. Acad. Sci. USA"},{"key":"ref_14","doi-asserted-by":"crossref","first-page":"306","DOI":"10.1016\/j.neuroimage.2004.09.018","article-title":"Predominantly Extra-Retinotopic Cortical Response to Pattern Symmetry","volume":"24","author":"Tyler","year":"2005","journal-title":"Neuroimage"},{"key":"ref_15","doi-asserted-by":"crossref","first-page":"259","DOI":"10.1080\/20445911.2016.1271804","article-title":"The Neural Basis of Mirror Symmetry Detection: A Review","volume":"29","author":"Cattaneo","year":"2017","journal-title":"J. Cogn. Psychol."},{"key":"ref_16","doi-asserted-by":"crossref","first-page":"1423","DOI":"10.1093\/cercor\/bhl054","article-title":"Face Configuration Processing in the Human Brain: The Role of Symmetry","volume":"17","author":"Chen","year":"2007","journal-title":"Cereb. Cortex"},{"key":"ref_17","doi-asserted-by":"crossref","first-page":"2133","DOI":"10.1097\/00001756-200007140-00015","article-title":"Perception of Mirror Symmetry Reveals Long-Range Interactions between Orientation-Selective Cortical Filters","volume":"11","author":"Saarinen","year":"2000","journal-title":"NeuroReport"},{"key":"ref_18","doi-asserted-by":"crossref","first-page":"79","DOI":"10.1163\/156856895X00124","article-title":"Multiple Mechanisms for the Detection of Mirror Symmetry","volume":"9","author":"Tyler","year":"1995","journal-title":"Spat. Vis."},{"key":"ref_19","doi-asserted-by":"crossref","unstructured":"Tyler, C.W., and Hardage, L. (2002). Human Symmetry Perception and Its Computational Analysis, Psychology Press.","DOI":"10.4324\/9781410606600"},{"key":"ref_20","doi-asserted-by":"crossref","first-page":"363","DOI":"10.1016\/0006-8993(79)90699-1","article-title":"Visual areas in the temporal cortex of the macaque","volume":"178","author":"Desimone","year":"1979","journal-title":"Brain Res."},{"key":"ref_21","doi-asserted-by":"crossref","first-page":"1182","DOI":"10.1093\/cercor\/11.12.1182","article-title":"Estimating Receptive Field Size from FMRI Data in Human Striate and Extrastriate Visual Cortex","volume":"11","author":"Smith","year":"2001","journal-title":"Cereb. Cortex"},{"key":"ref_22","doi-asserted-by":"crossref","first-page":"1101","DOI":"10.3758\/BF03206161","article-title":"Symmetry and Selective Attention: A Dissociation between Effortless Perception and Serial Search","volume":"60","author":"Olivers","year":"1998","journal-title":"Percept. Psychophys."},{"key":"ref_23","doi-asserted-by":"crossref","first-page":"95","DOI":"10.1177\/0956797617729808","article-title":"Symmetric objects become special in perception because of generic computations in neurons","volume":"29","author":"Pramod","year":"2018","journal-title":"Psychol. Sci."},{"key":"ref_24","doi-asserted-by":"crossref","first-page":"7","DOI":"10.1167\/1.2.7","article-title":"The Symmetry Magnification Function Varies with Detection Task","volume":"1","author":"Tyler","year":"2001","journal-title":"J. Vis."},{"key":"ref_25","doi-asserted-by":"crossref","first-page":"659","DOI":"10.1098\/rspb.1998.0344","article-title":"The Spatial Region of Integration for Visual Symmetry Detection","volume":"265","author":"Dakin","year":"1998","journal-title":"Proc. R. Soc. Lond. Ser. B Biol. Sci."},{"key":"ref_26","doi-asserted-by":"crossref","first-page":"2041669520913052","DOI":"10.1177\/2041669520913052","article-title":"Seven Myths on Crowding and Peripheral Vision","volume":"11","author":"Strasburger","year":"2020","journal-title":"i-Perception"},{"key":"ref_27","unstructured":"Traquair, H.M. (1927). An Introduction to Clinical Perimetry, Henry Kimpton Publisher."},{"key":"ref_28","doi-asserted-by":"crossref","unstructured":"Contreras-Vidal, J.L., Robleto, D., Cruz-Garza, J.G., Azor\u00edn, J.M., and Nam, C.S. (2019). Mobile Brain-Body Imaging and the Neuroscience of Art, Innovation and Creativity, Springer International Publishing.","DOI":"10.1007\/978-3-030-24326-5"},{"key":"ref_29","doi-asserted-by":"crossref","first-page":"364","DOI":"10.1207\/s15327957pspr0804_3","article-title":"Processing Fluency and Aesthetic Pleasure: Is Beauty in the Perceiver\u2019s Processing Experience?","volume":"8","author":"Reber","year":"2004","journal-title":"Pers. Soc. Psychol. Rev."},{"key":"ref_30","unstructured":"Cohen, J. (1988). Statistical Power Analysis for the Behavioral Sciences, L. Erlbaum Associates. [2nd ed.]."},{"key":"ref_31","unstructured":"Champely, S. (2020). Pwr: Basic Functions for Power Analysis, Available online: https:\/\/cran.r-project.org\/web\/packages\/pwr\/."},{"key":"ref_32","doi-asserted-by":"crossref","first-page":"200","DOI":"10.1016\/j.tics.2019.12.009","article-title":"Avoid Cohen\u2019s \u2018Small\u2019, \u2018Medium\u2019, and \u2018Large\u2019 for Power Analysis","volume":"24","author":"Correll","year":"2020","journal-title":"Trends Cogn. Sci."},{"key":"ref_33","doi-asserted-by":"crossref","first-page":"195","DOI":"10.3758\/s13428-018-01193-y","article-title":"PsychoPy2: Experiments in Behavior Made Easy","volume":"51","author":"Peirce","year":"2019","journal-title":"Behav. Res."},{"key":"ref_34","doi-asserted-by":"crossref","first-page":"90","DOI":"10.1109\/MCSE.2007.55","article-title":"Matplotlib: A 2D Graphics Environment","volume":"9","author":"Hunter","year":"2007","journal-title":"Comput. Sci. Eng."},{"key":"ref_35","unstructured":"R Core Team (2013). R: A Language and Environment for Statistical Computing, R Foundation for Statistical Computing. Available online: http:\/\/www.R-project.org\/."},{"key":"ref_36","doi-asserted-by":"crossref","first-page":"39","DOI":"10.3928\/0191-3913-19680201-10","article-title":"Saccadic and Pursuit Systems: A Review","volume":"5","author":"Miller","year":"1968","journal-title":"J. Pediatr. Ophthalmol. Strabismus"},{"key":"ref_37","doi-asserted-by":"crossref","first-page":"6","DOI":"10.1167\/6.12.6","article-title":"The Speed of Visual Attention: What Time Is It?","volume":"6","author":"Carlson","year":"2006","journal-title":"J. Vis."},{"key":"ref_38","doi-asserted-by":"crossref","first-page":"345","DOI":"10.3389\/fnhum.2020.00345","article-title":"A Theoretical Framework for How We Learn Aesthetic Values","volume":"14","author":"Aleem","year":"2020","journal-title":"Front. Hum. Neurosci."},{"key":"ref_39","doi-asserted-by":"crossref","first-page":"823","DOI":"10.1068\/p5249","article-title":"An Information Theory Analysis of Visual Complexity and Dissimilarity","volume":"35","author":"Donderi","year":"2006","journal-title":"Perception"},{"key":"ref_40","doi-asserted-by":"crossref","unstructured":"Correa-Herran, I., Aleem, H., and Grzywacz, N.M. (2020). Evolution of Neuroaesthetic Variables in Portrait Paintings throughout the Renaissance. Entropy, 22.","DOI":"10.3390\/e22020146"},{"key":"ref_41","first-page":"112","article-title":"Liking versus Complexity: Decomposing the Inverted U-Curve","volume":"10","author":"Jacobs","year":"2016","journal-title":"Front. Hum. Neurosci."},{"key":"ref_42","doi-asserted-by":"crossref","first-page":"3121","DOI":"10.1016\/S0042-6989(00)00157-7","article-title":"Signal Detection Theory in the 2AFC Paradigm: Attention, Channel Uncertainty and Probability Summation","volume":"40","author":"Tyler","year":"2000","journal-title":"Vis. Res."},{"key":"ref_43","doi-asserted-by":"crossref","unstructured":"Andrews, L.C. (1998). Special Functions of Mathematics for Engineers, SPIE Press.","DOI":"10.1117\/3.270709"},{"key":"ref_44","doi-asserted-by":"crossref","first-page":"1355","DOI":"10.3758\/s13414-023-02672-x","article-title":"The Intrinsic Variance of Beauty Judgment","volume":"85","author":"Pombo","year":"2022","journal-title":"Atten. Percept. Psychophys."},{"key":"ref_45","doi-asserted-by":"crossref","unstructured":"Rousseeuw, P.J., and Leroy, A.M. (1987). Robust Regression and Outlier Detection, Wiley.","DOI":"10.1002\/0471725382"},{"key":"ref_46","doi-asserted-by":"crossref","first-page":"308","DOI":"10.1093\/comjnl\/7.4.308","article-title":"A Simplex Method for Function Minimization","volume":"7","author":"Nelder","year":"1965","journal-title":"Comput. J."},{"key":"ref_47","doi-asserted-by":"crossref","first-page":"3","DOI":"10.1007\/s10107-015-0892-3","article-title":"Coordinate Descent Algorithms","volume":"151","author":"Wright","year":"2015","journal-title":"Math. Program."},{"key":"ref_48","first-page":"13287","article-title":"The Continuous Bernoulli: Fixing a Pervasive Error in Variational Autoencoders","volume":"32","author":"Cunningham","year":"2019","journal-title":"Adv. Neural Inf. Process. Syst."},{"key":"ref_49","doi-asserted-by":"crossref","unstructured":"Bertamini, M., Makin, A., and Pecchinenda, A. (2013). Testing Whether and When Abstract Symmetric Patterns Produce Affective Responses. PLoS ONE, 8.","DOI":"10.1371\/journal.pone.0068403"},{"key":"ref_50","doi-asserted-by":"crossref","first-page":"4416","DOI":"10.1093\/cercor\/bhw255","article-title":"An Electrophysiological Index of Perceptual Goodness","volume":"26","author":"Makin","year":"2016","journal-title":"Cereb. Cortex"},{"key":"ref_51","doi-asserted-by":"crossref","first-page":"e7078","DOI":"10.7717\/peerj.7078","article-title":"Symmetry Preference in Shapes, Faces, Flowers and Landscapes","volume":"7","author":"Bertamini","year":"2019","journal-title":"PeerJ"},{"key":"ref_52","doi-asserted-by":"crossref","first-page":"R378","DOI":"10.1016\/j.cub.2022.03.002","article-title":"Aesthetics: It\u2019s Beautiful to Me","volume":"32","author":"Pombo","year":"2022","journal-title":"Curr. Biol."}],"container-title":["Symmetry"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/8\/1568\/pdf","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,10,10]],"date-time":"2025-10-10T20:31:23Z","timestamp":1760128283000},"score":1,"resource":{"primary":{"URL":"https:\/\/www.mdpi.com\/2073-8994\/15\/8\/1568"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[2023,8,11]]},"references-count":52,"journal-issue":{"issue":"8","published-online":{"date-parts":[[2023,8]]}},"alternative-id":["sym15081568"],"URL":"https:\/\/doi.org\/10.3390\/sym15081568","relation":{},"ISSN":["2073-8994"],"issn-type":[{"value":"2073-8994","type":"electronic"}],"subject":[],"published":{"date-parts":[[2023,8,11]]}}}