Creative Visualisation of Magic Squares

Magic squares are n*n square grids in which each row, column, and diagonal add to the same sum. The ‘magic line’, drawn by connecting each integer in numerical sequence, creates a pattern that can differ or be shared between instances. The dual purpose of this work is: 1. to produce a variety of artworks—printed, digital and animated that use the magic line as a departure point; and 2. to investigate mathematical processes (matrix transformations) that produce identical magic line patterns, with the aim of identifying all unique such patterns, and simplifying the classification of magic squares, using visual and programmatic methods. The ongoing creative process has led us to produce a web-based visualisation tool (squares.cubelife.org), with which we have explored different types of mathematical curve to visualise the magic line, and to identify certain useful groups. This can already produce an extensive variety of interesting aesthetic results that differ from existing ‘straight line’ visualisations of magic squares. As well as exploring the creative visual permutations, our methods also enable the measurement of certain properties, such as the length of the magic line and the results of certain transformations.

Content

Author and article information

Contributors

Dave Everitt

Fania Raczinski

Conference

Publication date: July 2020

Publication date (Print): July 2020

Pages: 217-224

Affiliations

[0001]Institute of Creative Technologies

De Montfort University

The Gateway

Leicester LE1 9BH, UK

Article

DOI: 10.14236/ewic/EVA2020.39

SO-VID: ec68f646-d76e-4961-986e-1aa83123d146

License:

This work is licensed under a Creative Commons Attribution 4.0 Unported License. To view a copy of this license, visit http://creativecommons.org/licenses/by/4.0/

Conference name: Proceedings of EVA London 2020

Conference acronym: EVA 2020

Conference number: 30

Conference location: London

Conference date: 6th July – 9th July 2020

Conference sponsor: Electronic Workshops in Computing (eWiC)

Conference theme: AI and the Arts: Artificial Imagination

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1477-9358 BCS Learning & Development

Self URI (article page): https://www.scienceopen.com/hosted-document?doi=10.14236/ewic/EVA2020.39

Self URI (journal page): https://ewic.bcs.org/

REFERENCES

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V BabyT Banz Vera Molnar http://www.veramolnar.com/ 08 February 2020
H.E Dudeney 1917 Amusements in Mathematics Project Gutenberg https://www.gutenberg.org/files/16713/16713-h/16713-h.htm 17 March 2020
A Dürer 1514 Melencolia I [engraving] National Gallery of Art Washington, DC https://www.nga.gov/collection/highlights/durer-melencolia.html 21 March 2020
E EdmondsD EverittM MacaulayG Turner 2004 On physiological computing with an application in interactive art Interacting with Computers 16 897 915
D EverittB Daglish 3D magic cube viewer https://daveeveritt.org/cube-app/magic_cube.html 15 March 2020
D EverittG Turner 1999 CubeLife https://cubelife.org/ 15 March 2020
D Everitt 2011 Is Creativity a 'natural' process? R AscottM Girao Presence in the Mindfield: Art, Identity and the Technology of Transformation Lisbon, Portugal Artshare-Universidade de Aveiro 103 107
D EverittF Raczinski 2019 880 in Interact’19 Digital Open [Exhibition] Lightbox Gallery, LCB Depot Leicester 4-20 December 2019
D EverittA Robertson 2007 Emergence and complexity: some observations and reflections on transdisciplinary research involving performative contexts and new media In the International Journal of Performance Arts and Digital Media November 2007
F Gaspalou Structure of Magic and Semi-Magic Squares, Methods and Tools for Enumeration https://www.gaspalou.fr/magic-squares/order-4.htm 06 March 2020
A Grogono 2010 The 6x6 Magic Squares https://www.grogono.com/magic/6x6.php 11 March 2020
A Grogono 2010 Numbers and Formulae for Regular Prime Number Squares https://www.grogono.com/magic/howmany.php-Numbers 15 March 2020
S Happersett 2014 Bridges Math Art Conference Seoul Fibonaccisusan https://fibonaccisusan.com/tag/seoul/ 12 March 2020
H Heinz 2010 Order 4, Transformations & Patterns http://www.magic-squares.net/transform.htm 15 March 2020
P Heimbach Magische Quadrate http://www.paulheimbach.de/quadrate/index.html 08 February 2020
M Kepner MEK Visysuals http://mekvisysuals.yolasite.com/ 15 March 2020
M Kepner 2017 Twinned Magic Vessels of Order 8 and The Five Faces of Jaenisch Mathematical Art Galleries http://gallery.bridgesmathart.org/exhibitions/2018-joint-mathematics-meetings/renpek1010 15 March 2020
D Lange 2013 ReCode | Hommage à Vera Molnar à Dürer https://www.flickr.com/photos/dianalange/albums/72157634470122110 08 February 2019
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P Maxwell Davies 1975 Ave Maris Stella http://petermaxwelldavies.com/?works_catalogue_entr=ave-maris-stella-63 15 March 2020
P Maxwell Davies 1977 A Mirror of Whitening Light http://petermaxwelldavies.com/?works_catalogue_entr=a-mirror-of-whitening-light-75 15 March 2020
MET (The Metropolitan Museum of Art) 2020 Heilbrunn Timeline of Art History: Melencolia I https://www.metmuseum.org/toah/works-ofart/43.106.1/ 21 March 2020
R McGregor 2004 Star Square and Circle: aspects of compositional process in Peter Maxwell Davies’s Ave Maris Stella Max Day mini conference, December 2004, University of Manchester
J Moran 1982 The Wonders of Magic Squares New York Random House
N Neel 2012 Charms, Amulets and Talismans https://www.prophet666.com/2012/08/charms-amulets-and-talismans.html 16 March 2020
F Raczinski 2020 Magic-SVG https://github.com/fania/magic-SVG 10 February 2020
G.E Roberts 2016 From Music to Mathematics: Exploring the Connections Johns Hopkins University Press
C Rivera 2019 The PDF version of the web pages by Mutsumi Suzuki for magic squares https://www.primepuzzles.net/thepuzzlers/MutsumiSuzuki’sMagicSquaresWebPages.pdf 15 March 2020
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W Trump 2019 How many magic squares are there? https://www.trump.de/magic-squares/howmany.html 11 March 2020
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Sōyetsu Yanagi 2013 Pattern chapter in The unknown craftsman Kodansha New York

Comments

Comment on this article

[1] H.C Agrippa 1533 Three Books of Occult Philosophy http://esotericarchives.com/agrippa/agripp2b.htm-chap22 15 March 2020

[2] V BabyT Banz Vera Molnar http://www.veramolnar.com/ 08 February 2020

[3] H.E Dudeney 1917 Amusements in Mathematics Project Gutenberg https://www.gutenberg.org/files/16713/16713-h/16713-h.htm 17 March 2020

[4] A Dürer 1514 Melencolia I [engraving] National Gallery of Art Washington, DC https://www.nga.gov/collection/highlights/durer-melencolia.html 21 March 2020

[5] E EdmondsD EverittM MacaulayG Turner 2004 On physiological computing with an application in interactive art Interacting with Computers 16 897 915

[6] D EverittB Daglish 3D magic cube viewer https://daveeveritt.org/cube-app/magic_cube.html 15 March 2020

[7] D EverittG Turner 1999 CubeLife https://cubelife.org/ 15 March 2020

[8] D Everitt 2011 Is Creativity a 'natural' process? R AscottM Girao Presence in the Mindfield: Art, Identity and the Technology of Transformation Lisbon, Portugal Artshare-Universidade de Aveiro 103 107

[9] D EverittF Raczinski 2019 880 in Interact’19 Digital Open [Exhibition] Lightbox Gallery, LCB Depot Leicester 4-20 December 2019

[10] D EverittA Robertson 2007 Emergence and complexity: some observations and reflections on transdisciplinary research involving performative contexts and new media In the International Journal of Performance Arts and Digital Media November 2007

[11] F Gaspalou Structure of Magic and Semi-Magic Squares, Methods and Tools for Enumeration https://www.gaspalou.fr/magic-squares/order-4.htm 06 March 2020

[12] A Grogono 2010 The 6x6 Magic Squares https://www.grogono.com/magic/6x6.php 11 March 2020

[13] A Grogono 2010 Numbers and Formulae for Regular Prime Number Squares https://www.grogono.com/magic/howmany.php-Numbers 15 March 2020

[14] S Happersett 2014 Bridges Math Art Conference Seoul Fibonaccisusan https://fibonaccisusan.com/tag/seoul/ 12 March 2020

[15] H Heinz 2010 Order 4, Transformations & Patterns http://www.magic-squares.net/transform.htm 15 March 2020

[16] P Heimbach Magische Quadrate http://www.paulheimbach.de/quadrate/index.html 08 February 2020

[17] M Kepner MEK Visysuals http://mekvisysuals.yolasite.com/ 15 March 2020

[18] M Kepner 2017 Twinned Magic Vessels of Order 8 and The Five Faces of Jaenisch Mathematical Art Galleries http://gallery.bridgesmathart.org/exhibitions/2018-joint-mathematics-meetings/renpek1010 15 March 2020

[19] D Lange 2013 ReCode | Hommage à Vera Molnar à Dürer https://www.flickr.com/photos/dianalange/albums/72157634470122110 08 February 2019

[20] P Maxwell Davies 2017 On Music, Mathematics and Magic Squares Peter Maxwell Davies Selected Writings Nicholas Jones Cambridge University Press P217

[21] P Maxwell Davies 1975 Ave Maris Stella http://petermaxwelldavies.com/?works_catalogue_entr=ave-maris-stella-63 15 March 2020

[22] P Maxwell Davies 1977 A Mirror of Whitening Light http://petermaxwelldavies.com/?works_catalogue_entr=a-mirror-of-whitening-light-75 15 March 2020

[23] MET (The Metropolitan Museum of Art) 2020 Heilbrunn Timeline of Art History: Melencolia I https://www.metmuseum.org/toah/works-ofart/43.106.1/ 21 March 2020

[24] R McGregor 2004 Star Square and Circle: aspects of compositional process in Peter Maxwell Davies’s Ave Maris Stella Max Day mini conference, December 2004, University of Manchester

[25] J Moran 1982 The Wonders of Magic Squares New York Random House

[26] N Neel 2012 Charms, Amulets and Talismans https://www.prophet666.com/2012/08/charms-amulets-and-talismans.html 16 March 2020

[27] F Raczinski 2020 Magic-SVG https://github.com/fania/magic-SVG 10 February 2020

[28] G.E Roberts 2016 From Music to Mathematics: Exploring the Connections Johns Hopkins University Press

[29] C Rivera 2019 The PDF version of the web pages by Mutsumi Suzuki for magic squares https://www.primepuzzles.net/thepuzzlers/MutsumiSuzuki’sMagicSquaresWebPages.pdf 15 March 2020

[30] W3C 2011 The quadratic Bézier curve commands in Scalable Vector Graphics (SVG) 1.1 (Second Edition) World Wide Web Consortium https://www.w3.org/TR/SVG11/paths.html#PathDataQuadraticBezierCommands 18 March 2020

[31] O Thurley 2012 Magic Squares http://oliverthurley.co.uk/blog/2012/10/magic-squares/

[32] W Trump 2018 Number of classic magic squares http://www.trump.de/magic-squares/normal.htm 08 March 2020

[33] W Trump 2019 How many magic squares are there? https://www.trump.de/magic-squares/howmany.html 11 March 2020

[34] E. W Weisstein 2020 Dihedral Group D4 MathWorld – A Wolfram Web Resource https://mathworld.wolfram.com/DihedralGroupD4.html 18 March 2020

[35] Sōyetsu Yanagi 2013 Pattern chapter in The unknown craftsman Kodansha New York

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