Abstract
This chapter is motivated by a question I asked myself: “How can combinatorial structures be used in a work of art?” Immediately, other questions arose: Are there artists that work or think combinatorially? If so, what works have they produced in this way? What are the similarities and differences between artworks produced using combinatorics? Combinatorics is a very transversal branch of mathematics. It is connected to logic, and it intervenes in the building of languages in general as natural language, musical language, and poetry. Combinatorics has been present in artistic practice for millenia, especially in music and poetry; for instance, in the shaped poems of Simmias of Rhodes in Ancient Greece. However, we are interested in artistic practices that are driven by the use of combinatorial ideas, structures, and methodologies, artists whose work is conceptualized or merely inspired by combinatorics. This often happens in connection with an interest in structure and language, and the phenomenon was significant in the twentieth century, as a by-product of the revolution that took place not only in art but in many other areas of knowledge. In this chapter, we present a survey of artists that think combinatorially, work combinatorially, and construct combinatorial artworks. The selection covers music, literature, visual arts including digital art, and an example of early physical interactive art, dance, theatre, and cinema. It is a non-exhaustive list of artists, selected to show differences and similarities in their ways of approaching art when using combinatorics.
Access this chapter
Tax calculation will be finalised at checkout
Purchases are for personal use only
Similar content being viewed by others
References
Bailey RW (1973) Computer poems. Potagannissing Press, Michigan
Bellamann H (1933) Charles Ives: the man and his music. Music Q 19(1):45–58
Bense M (1956) Aesthetica II – aesthetische information. Agis-Verlag, Baden-Baden
Benson D (2006) Music: a mathematical offering. Cambridge University Press, Cambridge
Berenguer Martín J (2007) Fundamentos epistemológicos de la permutación en la poesía de Juan Eduardo Cirlot. Anuario de filología hispánica 10:69–81
Berge C (2016) Para un análisis potencial de la literatura combinatoria. In: Salceda H (ed) OULIPO. Atlas de Literatura Potencial, 1: Ideas Potentes. Pepitas de Calabaza, Logroño
Bernard JW (1988) The evolution of Elliott Carter’s rhythmic practice. Perspect New Music 26(2):164–203
Bill M (1996) The mathematical approach in contemporary art. In: Stiles K, Selz P (eds) Theories and documents of contemporary art. A Sosurcebook of Artists’ Writings, University of California Press, Berkeley, pp 74–77
Bither P, Engberg S (2011) Philip Glass and Lucinda Childs Discuss “Dance” (video). Walker Art Center. https://www.youtube.com/watch?v=LBcAEmIn19g. Accessed 24 Sept 2020
Bonačić V (1974) Kinetic art: application of abstract algebra to objects with computer-controlled flashing lights and sound combinations. Leonardo 7(3):193–200
Bonch-Osmolovskaya T (2018) Combinatorial greetings from Georges Perec. In: Torrence B, Torrence E, Séquin CH, Fenyvesi K, Kaplan CS (eds) Proceedings of Bridges Stockholm 2018: Mathematics, Music, Architecture, Education, Culture, Stockholm, 25–29 July 2018. Tessellations Publishing, Phoenix, pp 253–258
Brits B (2019) Beckett and mathematics. In: Rabaté JM (ed) The new Samuel Beckett studies. Cambridge University Press, Cambridge, pp 215–230
Burrows J (2020) Jonathan Burrows’ website http://www.jonathanburrows.info. Accessed 24 Sept 2020
Calvino I (1968) Cibernetica e fantasmi (Appunti sulla narrativa come processo combinatorio). In: Le conferenze dell’Associazione Culturale Italiana 1967–68, Torino, pp 9–23
Calvino I (1987) Comment j’ai écrit un de mes livres. In: La Bibliotèque Oulipienne, vol 2. Ramsay, pp 24–44
Cameron PJ (1994) Combinatorics: topics, techniques, algorithms. Cambridge University Press, Cambridge
Carter E (2001) Harmony book. Carl Fisher, New York
Copeland R (1999) Cunningham, collage, and the computer. PAJ J Perform Art 21(3):42–54
Copeland R (2002) Merce Cunningham and the aesthetic of collage. Drama Rev 46(1):11–28
Corbett J (1998) Nothing is true; everything is permuted: the Brion Gysin/Steve Lacy songbook. Discourse 20(1/2):110–123
Cowell H (1969) New musical resources. Something Else Press, New York
Cunningham M (1994) Four events that have led to large discoveries. In: Vaughan D, Harris M (eds) Merce Cunningham: fifty years. Aperture Press, New York, p 276
D’Ors M (1977) El Caligrama de Simmias a Apollinaire. Historia y antología de una tradición clásica. Universidad de Navarra, Pamplona
Edwards JS (2005) The Carmina of publilius optatianus porphyrius and the creative process. In: Deroux C (ed) Studies in latin literature and roman history, vol XII. Collection Latomus, Bruxelles, pp 447–466
Fages F (2020) Personal communication
Fargion M (2020) Matteo Fargion’s website https://www.matteofargion.com. Accessed 24 Sept 2020
Fritz D (2008) Vladimir Bonačić: computer-generated works made within Zagreb’s new tendencies network (1961–1973). Leonardo 41(2):175–183
Fritz D (2011) Images and sound created and synchronized by algorithm Vladimir Bonačić’s computer-generated interactive audiovisual object GF. E(16,4), 1969–1974. In: Proceedings of the International Conference Pierre Schaeffer: MediArt, Rijeka, 2011. Museum of Modern and Contemporary Art, Rijeka, pp 134–143
Funkhouser CT (2007) Prehistoric digital poetry. An archaeology of forms, 1959–1995. The University of Alabama Press, Tuscaloosa
Greenaway P (2005) Some organizing principles. In: Emmer M (ed) The visual mind II. The MIT Press, Cambridge, pp 601–622
Hapke T (2012) Wilhelm Ostwald’s combinatorics as a link between in-formation and form. Libr Trends 61(2):286–303
Hay D, McDonagh D (1970) Interview with Deborah Hay. (2 audio disks)
Higgins D (1987) Pattern poetry: guide to an unknown literature. SUNY Press, Albany
Hoff A (2020) Anders Hoff a.k.a. inconvergent’s website https://inconvergent.net. Accessed 24 Sept 2020
Howard JA (1994) The roots of Beckett’s aesthetic: mathematical allusions in ‘Watt.’ (Samuel Beckett). Papers Lang Lit 30(4):346–351
I love e-poetry (webpage). http://iloveepoetry.com/. Accessed 24 Sept 2020
Janés C (2014) Juan Eduardo Cirlot. Cuando la palabra y la letra llaman a su forma. Tintas. Quaderni di letterature iberiche e iberoamericane Special issue pp 389–400
Jennings G (2015) Abstract video. The moving image in contemporary art. University of Clifornia Press, Oakland
Johnson T (2020a) Editions 75 – works by Tom Johnson. http://www.editions75.com/. Accessed 24 Sept 2020
Johnson T (2020b) Tom Johnson – Youtube. http://www.youtube.com/channel/UCUJX3s4zL0tc2vgnCNpDjAg. Accessed 24 Sept 2020
Johnson T, Jedrzejewski F (2014) Looking at numbers. Birkhäuser, Basel
Kaprow A (1993) Essays on the blurring of art and life. University of California Press, Berkeley
Keefer C, Guldemond J (2013) Oskar Fischinger 1900–1967. In: Experiments in cinematic abstraction. EYE Filmmuseum, Amsterdam
Knoblock E (2002) The sounding algebra: relations between combinatorics and music from Mersenne to Euler. In: Assayag G, Feichtinger HG, Rodrigues JF (eds) Music and mathematics. A diderot mathematical forum. Springer, Berlin/Heidelberg
Kuri JF (ed) (2003) Brion Gysin: tuning in to the multimedia age. Thames and Hudson, New York
Lambert JP (1990) Interval cycles as compositional resources in the music of Charles Ives. Music Theory Spect 12(1):43–82
LeWitt S (1967a) Serial project #1. Aspen 5–6, 1967. http://www.ubu.com/aspen/aspen5and6/serialProject.html. Accessed 24 Sept 2020
LeWitt S (1967b) Paragraphs on conceptual art. Artforum June 1967
LeWitt S (1969) Sentences on conceptual art. Art-Language 1(1)
LeWitt S, Garrels G (2011) Untangling the puzzle of Sol LeWitt’s open cubes (video). San Francisco Museum of Modern Art. https://www.youtube.com/watch?v=w9ROCnWMPww
Lorenzi MG, Francaviglia M (2011) The role of mathematics in contemporary art at the turn of the millenium. Aplimat – J Appl Math 4(4):215–238
Loy G (2006) Musimathics. The mathematical foundations of music, vol 1. The MIT Press, Cambridge
MacDonald S (1979) Interview with Hollis Frampton: “Zorns Lemma”. Q Rev Film Stud 4(1): 23–37
Martí Ortega E (2012) Juan Eduardo Cirlot y las golondrinas de Bécquer. Cuad Hispanoam 747: 39–48
Maurer WD (2004) The mathematics of Jazz. In: Sarhangi R, Séquin C (eds) Proceedings of Bridges 2004: Mathematical Connections in Art, Music, and Science, Winfield, Kansas. Central Plain Book Manufacturing, Winfield, Kansas, pp 273–280
McCormack J, d’Inverno M (eds) (2012) Computers and creativity. Springer, Berlin/Heidelberg
Menabrea LF (1843) Sketch of the analytical engine invented by Charles Babbage. R and JE Taylor, London
Meštrović M (2005) Rendering scientific as the condition for humanization. In: From the particular to the general, Mladost, Zagreb. (Originally in the catalog of Nove Tendencije 2, 1963)
Migayrou F (ed) (2018) Coder le Monde. Éditions du Centre Pompidou, Paris
Mohr M (1971) Computer graphics. Une ésthetique programmée. Weberdruck, Pforzheim
Mohr M (2019) Personal communication
Mohr M (2020a) Manfred Mohr’s website. http://www.emohr.com/. Accessed 24 Sept 2020
Mohr M (2020b) Manfred Mohr’s vimeo video channel. https://vimeo.com/manfredmohr. Accessed 24 Sept 2020
Molnar V (1984) Regard sur mes images. Revue d’esthétique 7:116
Molnar V (2020) Vera Molnar. http://www.veramolnar.com/. Accessed 24 Sept 2020
Nolan C (2000) On musical space and combinatorics: historical and conceptual perspectives in music theory. In: Sarhangi R (ed) Bridges. Mathematical connections in art, music, and science. Winfield, Kansas, pp 201–208
Paul C (ed) (2016) A companion to digital art. Wiley Blackwell, Oxford
Perec G (1976) Georges Perec présente La Vie mode d’emploi (video). Institut Nationale de l’Audiovisuel. Available online: https://www.ina.fr/video/I09365760/georges-perec-presente-la-vie-mode-d-emploi-video.html. Accessed 24 Sept 2020
Perec G (1981) Quatre figures pour La Vie mode d’emploi. L’Arc 76:50–54
Polanski L, Barnett A, Winter M (2011) A few more words about James Tenney: dissonant counterpoint and statistical feedback. J Math Music 5(2):63–82
Ragona M (2004) Hidden noise: strategies of sound Montage in the films of Hollis Frampton. October 109:96–118
Read RC (1997) Combinatorial problems in the theory of music. Discr Math 167–168:543–551
Rottman M (2015) Donald Judd’s arithmetics and Sol LeWitt’s combinatorics. On the relationship between visual and mathematical in New York art around 1960. In: Emmer M (ed) Imagine math 3. Between culture and mathematics. Springer, Cham
Saunders J (2008) Modular music. Perspect New Music 46(1):152–193
Schoenberg A (1975) Composition with twelve tones. In: Schoenberg A (ed) Style and idea. Selected writings of Arnold Schoenberg. Faber & Faber, London, pp 102–143
Sethares WA (2007) Rhythm and transforms. Springer, London
Shanken E (ed) (2009) Art and electronic media. Paidon Press, New York
Stevens B (2010) A purgatorial calculus: Beckett’s mathematics in “Quad”. In: Gontarski SE (ed) A companion to Samuel Beckett. Wiley-Blackwell, Chischester, pp 164–181
Stinson DR (2004) Combinatorial designs: constructions and analysis. Springer, New York
Swift J (1735) Gulliver travel’s. Available at the Internet Archive: https://archive.org/details/thetravelsofdoctorlemuelgulliverintoremotenationsoftheworld. Accessed 24 Sept 2020
Vásquez Rocca A (2013) Diálogo de exiliados, cine y políticas estéticas en Latinoamérica: Raúl Ruiz, territorios, ontología de lo fantástico y polisemia visual. Nómadas. Crit J Soc Juridical Sci 187–211. https://dialnet.unirioja.es/servlet/articulo?codigo=4232804
Vega A, Weibel P, Zielinski S (2018) DIA-LOGOS. Ramon Llull and the Ars Combinatoria (brochure). ZKM | Center for Art and Media, Karlsruhe. https://zkm.de/media/file/en/dialogos_broschure-en_digital.pdf. Accessed 24 Sept 2020
Vriezen S (2017) Diagrams, games and time (Towards the analysisi of open form scores). In: Pareyon G, Pina-Romero S, Agustín-Aquino OA, Lluis-Puebla E (eds) The musical-mathematical mind. Patterns and transformations. Springer, Cham
Vriezen S (2020) Personal communication
Weiss J (1991) Writing at risk: interviews in Paris with uncommon writers. University of Iowa Press, Iowa City
Winter M (2019) A few more thoughts about Leibniz: the prediction of harmonic distance in harmonic space. MusMat Braz J Music Math 3:79–92
Xenakis I (1971) Formalized music: thought and mathematics in composition. Pendragon Press, Styuvesant
Zweig J (1997) Ars combinatoria: mystical systems, procedural art, and the computer. Art J 56(3):20–29
Author information
Authors and Affiliations
Corresponding author
Editor information
Editors and Affiliations
Rights and permissions
Copyright information
© 2021 Springer Nature Switzerland AG
About this entry
Cite this entry
Barrière, L. (2021). Combinatorial Artists: Counting, Permutations, and Other Discrete Structures in Art. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-57072-3_132
Download citation
DOI: https://doi.org/10.1007/978-3-319-57072-3_132
Published:
Publisher Name: Springer, Cham
Print ISBN: 978-3-319-57071-6
Online ISBN: 978-3-319-57072-3
eBook Packages: Mathematics and StatisticsReference Module Computer Science and Engineering