Symmetry is a fundamental principle in aesthetics, and is present in some of humankind's creations from very early times.

Here are two interesting articles about the early evidence:

Hodgson, Derek

2008 “An ‘aesthetic’ explanation for the symmetry of Acheulian handaxes: some neuropsychological insights,” in Plasticités Sciences Arts (http://www.plasticites-sciences-arts.org/PLASTIR/Hodgson%20P12.pdf, uploaded: 22 September 2008, accessed: 2 April 2015).

2011 “The first appearance of symmetry in the human lineage: where perception meets art,” in Symmetry (MDPI AG), vol. 3, no. 1, pp. 37-53 (http://www.mdpi.com/2073-8994/3/1/37, uploaded: 1 March 2011, accessed: 30 January 2015).

Painting is two dimensional, so the idea of a successive phrase needs to take into account the fact that in music we hear sounds in a set sequence, whereas in painting and other visual arts we see the artwork in two or three dimensions. This is a good article about comparing music and painting. (The title sounds quite negative about comparing music and art, but it isn't meant to be.)

https://philosophynow.org/issues/50/Why_Abstract_Painting_Isnt_Music

When viewing a painting (or objects from other classes of visual arts), especially when we are close to the work of art, we experience it over time, weaving a coherent experience from the successive perception of its parts. Eye-tracking devices, pioneered by Yarbus half a century ago, now permit the precise study of the role of eye movements in visual perception. Here are some publications that explore this fundamental aspect of aesthetic experience:

Böck, Angelika

1996 “Trans-parent, eye-tracking,” in Angelika Böck (http://www.angelika-boeck.de/en/works/eye-tracking/single-page-eyetracking/trans-parent/, accessed: 16 March 2017).

Brieber, David; Nadal, Marcos; Leder, Helmut; Rosenberg, Raphael

2014 “Art in time and space: context modulates the relation between art experience and viewing time,” in Plos One (Public Library of Science), vol. 9, no. 6 (http://www.plosone.org/article/info%3Adoi%2F10.1371%2Fjournal.pone.0099019, uploaded: 3 June 2014, accessed: 30 January 2015).

Brinkmann, Hanna; Commare, Laura; Leder, Helmut; Rosenberg, Raphael

2014 “Abstract art as a universal language?,” in Leonardo (MIT Press Journals), vol. 47, no. 3, pp. 256, 257 (https://www.researchgate.net/publication/265830368, accessed: 30 January 2015).

Foulsham, Tom; Kingstone, Alan

2010 “Asymmetries in the direction of saccades during perception of scenes and fractals: effects of image type and image features,” in Vision Research (Elsevier), vol. 50, no. 8, 7 April 2010, pp. 779-795 (http://ac.els-cdn.com/S0042698910000416/1-s2.0-S0042698910000416-main.pdf?_tid=224f94d0-a8d6-11e4-a0be-00000aacb35f&acdnat=1422660018_87aab3ce3a82b9334c5663475fe8479c, accessed: 30 January 2015).

Kapoula, Zoï; Adenis, M2012arie-Sarah; Lê, Thanh-Thuan; Yang, Qing; Lipede, Gabi

2011 “Pictorial depth increases body sway” (preliminary version), in Psychology of Aesthetics, Creativity, and the Arts (American Psychological Association), vol. 5, no. 2, pp. 186-193 (pp. 1-8 in this version) (http://iris.dr2.cnrs.fr/IMG/pdf_art_posture.pdf, accessed: 30 January 2015).

Kapoula, Zoï; Bucci, Maria Pia; Yang, Qing; Bacci, Francesca

2010 “Perception of space in Piero della Francesca’s Annunciation: an eye-movement and art-historical study,” in Leonardo (The International Society for the Arts, Sciences and Technology), vol. 43, no. 2, pp. 153-158 (http://iris.dr2.cnrs.fr/IMG/pdf/ZK_LEON4302_pp153-158_2010.pdf, accessed: 30 January 2015).

Kapoula, Zoï; Gintautas, Daunys; Herbez, Olivier; Yang, Qing

2009 “Effects of title on eye-movement exploration of cubist paintings by Fernand Léger,” in Perception (Pion), vol. 38, no. 4, pp. 479-491 (http://www.perceptionweb.com/fulltext_temp/0/p6080.pdf, accessed: 23 June 2015).

Kapoula, Zoï; Yang, Qing; Vernet, Marine; Bucci, Maria Pia

2009 “Eye movements and pictorial space perception: studies of paintings from Francis Bacon and Piero della Francesca,” in Cognitive Semiotics (De Gruyter Mouton), vol. 5, pp. 103-121 (http://www.degruyter.com/view/j/cogsem.2009.5.issue-fall2009/cogsem.2009.5.fall2009.103/cogsem.2009.5.fall2009.103.xml, accessed: 30 January 2015).

Lipps, Marianne; Pelz, Jeff B.

2004 “Yarbus revisited: task-dependent oculomotor behavior” (abstract), in Journal of Vision (Association for Research in Vision and Ophthamology), vol. 4, no. 8, article 115 (http://jov.arvojournals.org/article.aspx?articleid=2130754, uploaded: June 2004, accessed: 30 January 2015).

Nelson, Jonathan D.; Cottrell, Garrison W.; Movellan, Javier R.; Sereno, Martin I.

2004 “Yarbus lives: a foveated exploration of how task influences saccadic eye movement” (abstract), in Journal of Vision (Association for Research in Vision and Ophthamology), vol. 4, no. 8, article 741 (http://jov.arvojournals.org/article.aspx?articleid=2131449, uploaded: August 2004, accessed: 14 April 2017).

Pomplun, Marc; Ritter, Helga; Velichkovsky, Boris

1996 “Disambiguating complex visual information: towards communication of personal views of a scene,” in Perception (Pion), vol. 25, no. 8, pp. 931-948 (http://www.perceptionweb.com/fulltext_temp/0/p250931.pdf, accessed: 23 June 2015).

Quian Quiroga, Rodrigo; Pedreira, Carlos

2011 “How do we see art: an eye-tracker study,” in Frontiers in Human Neuroscience (Frontiers Media), vol. 5, article 98 (http://journal.frontiersin.org/article/10.3389/fnhum.2011.00098/full, uploaded: 12 September 2011, accessed: 8 August 2016).

Savazzi, Federica; Massaro, Davide; Di Dio, Cinzia; Gallese, Vittorio; Gilli, Gabriella; Marchetti, Antonella

2014 “Exploring responses to art in adolescence: a behavioral and eye-tracking study,” in Plos One (Public Library of Science), vol. 9, no. 7 (http://journals.plos.org/plosone/article?id=10.1371/journal.pone.0102888, uploaded: 21 July 2014, accessed: 31 January 2015).

Syaiou, Stella; Patias, Petros; Gelos, Leonidas; Ziogas, Yiannis

2013 “Exploring roads less traveled: eye-tracking studies in art,” in Re-New Digital Arts Festival, The Big Picture, The Confluence of Art, Science and Technology, at Copenhagen, Denmark, 29 October-1 November 2013 (https://www.researchgate.net/publication/258277478, accessed: 30 January 2015).

Tatler, Benjamin W.; Wade, Nicholas J.; Kwan, Hoi; Findlay, John M.; Velichkovsky, Boris M.

2010 “Yarbus, eye movements, and vision,” in i-Perception (Sage Publications), vol. 1, pp. 7-27 (http://journals.sagepub.com/doi/abs/10.1068/i0382, uploaded: 1 January 2010, accessed: 9 February 2017).

Tchalenko, John

2013 “Capturing life” (video), in Factum Foundation (http://www.factumfoundation.org/pag/212/John-Tchalenko-br-Capturing-Life, uploaded: 2013, accessed: 30 January 2015).

Wallraven, Christian; Cunningham, Douglas W.; Rigau, Jaume; Feixas, Miquel; Sbert, Mateu

2009 “Aesthetic appraisal of art - from eye movements to computers,” in Computational Aesthetics 2009, Eurographics Workshop on Computational Aesthetics in Graphics, Visualization, and Imaging, Dieter W. Fellner, Werner Hansmann, Werner Purgathofer, and François Sillion, editors, Ginebra, Eurographics Association, pp. 137-144 (http://www.kyb.mpg.de/fileadmin/user_uploaded/files/publications/CAe2009-Wallraven_5740[0].pdf, accessed: 30 January 2015).

Yarbus, Alfred L.

1967 Eye movements and vision, Basil Haigh, translator, New York: Plenum Press (http://wexler.free.fr/library/files/yarbus%20(1967)%20eye%20movements%20and%20vision.pdf, accessed: 30 January 2015).

Ylitalo, Anna-Kaisa; Särkkä, Aila; Guttorp, Peter

2016 “What we look at in paintings: a comparison between experienced and inexperienced art viewers” (preliminary version), in Annals of Applied Statistics (Institute of Mathematical Statistics), vol. 10, no. 2 (http://imstat.org/en/index.html, accessed: 16 April 2016).

Conference Paper Saccadic Universe: eye-gaze controlled navigation to the lan...

Article Abstract Art as a Universal Language?