Abstract
Cellular automata provide a natural way of exploring the intersection between mathematics and art, and many fiber arts provide natural ways of depicting cellular automata. We review some of the types of cellular automata, including elementary cellular automata, the Game of Life and “lifelike” cellular automata, and stranded cellular automata. We then provide a survey of many of the different ways that cellular automata have been used in fiber arts. This includes both depictions of well-known patterns produced by cellular automata and also cellular automata that were specifically designed or specifically chosen for their suitability in fiber media.
References
Ashton T (2011) Fashioning fine fractals from fiber. In: belcastro s-m, Yackel C (eds) Crafting by concepts, Chap 4. A K Peters/CRC Press, Natick, pp 58–86
Campbell MP (2002) Fractal crochet. http://www.marypat.org/stuff/nylife/020325.html. Accessed 10 Aug 2018
Collins J (2013) Chaotic knitting. https://botanicamathematica.wordpress.com/2013/03/18/chaotic-knitting/. Accessed 13 Jan 2019
Ellison EF (2009) Mathematical classroom quilts. In: Proceedings of Bridges 2009: mathematics, music, art, architecture, culture. Tarquin Publications, pp 341–342
Ellison EK (2018) Mathematical quilts. http://mathematicalquilts.com. Accessed 6 Oct 2018
Feijs L, Toeters M (2017) A cellular automaton for pied-de-poule (Houndstooth). In: Proceedings of Bridges 2017: mathematics, music, art, architecture, education, culture. Tessellations Publishing, pp 403–406
Fisher G (2016) Free beading pattern – sierpinski triangle. https://gwenbeads.blogspot.com/2016/10/free-beading-pattern-sierpinski-triangle.html. Accessed 18 Aug 2018
Fisher G (2020, Forthcoming) Bead weaving with algorithms. World Scientific Publishers
Fox C (2008) Cellular automata tea cozy – instructions. http://web.mit.edu/cfox/www/knitting/b.html. Accessed 10 Aug 2018
Gaughan N (2012) Knitting nature: 39 designs inspired by patterns in nature. Stewart, Tabori and Chang, New York/London
Griswold RE (2005) Cellular automata, part 1. Webside 10:3–4
Griswold RE (2004a) Drawdown automata, part 1: basic concepts, 8p. https://www2.cs.arizona.edu/patterns/weaving/webdocs/gre_dda1.pdf. Accessed 27 Oct 2018
Griswold RE (2004b) Drawdown automata, part 4: a few good rules, 4p. https://www2.cs.arizona.edu/patterns/weaving/webdocs/gre_dda4.pdf. Accessed 27 Oct 2018
Gross D (2013) Cellular automaton design for cross-stitch IPhone case. http://www.instructables.com/id/Cellular-Automaton-Design-for-Cross-Stitch-iPhone-/. Accessed 10 Aug 2018
Holden L (2014a) Knit stranded cellular automata. Sockupied, 10 Spring 2014
Holden L (2014b) Automata socks. Sockupied, 11 Spring 2014
Holden J (2017) The complexity of braids, cables, and weaves modeled with stranded cellular automata. In: Proceedings of Bridges 2017: mathematics, music, art, architecture, education, culture. Tessellations Publishing, pp 463–466
Holden J, Holden L (2016) Modeling braids, cables, and weaves with stranded cellular automata. In: Proceedings of Bridges 2016: mathematics, music, art, architecture, education, culture. Tessellations Publishing, pp 127–134
Kieran A (2013) Weaving Wolfram rule 90. https://edinburghhacklab.com/2013/12/weaving-wolfram-rule-90/. Accessed 18 Aug 2018
Lamb E (2015) Help make wearable cellular automata a thing. https://blogs.scientificamerican.com/roots-of-unity/help-make-wearable-cellular-automata-a-thing/. Accessed 10 Aug 2018
Matsumoto E, Segerman H, Serriere F (2018) Möbius cellular automata scarves. In: Proceedings of Bridges 2018: mathematics, music, art, architecture, education, culture. Tessellations Publishing, pp 523–526
Miller J (1970) Periodic forests of stunted trees. Phil Trans R Soc Lond A 266(1172):63–111
New D (1997) Celluar automaton knitting. Knitter’s Mag 49:82–83
New D (2003) Unexpected knitting. Schoolhouse Press, Stevens Point
Schiff JL (2008) Cellular automata: a discrete view of the world, 1st edn. Wiley, Hoboken
Thompson C (2006) A baby sweater generated by Conway’s “Game of Life”!. http://www.collisiondetection.net/mt/archives/2006/04/_as_a_principle.php. Accessed 13 Aug 2018
Thorp J (2012) Infinite weft (Exploring the old aesthetic). http://blog.blprnt.com/blog/blprnt/infinite-weft-exploring-the-old-aesthetic. Accessed 27 Oct 2018
Wildstrom DJ (2007) The sierpinski variations: self-similar crochet. In: belcastro s-m, Yackel C (eds) Making mathematics with needlework: ten papers and ten projects, Chap 3. A K Peters/CRC Press, Wellesley, pp 40–52
Wolfram S (2002) A new kind of science. Wolfram Media, Champaign
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Holden, J., Holden, L. (2020). A Survey of Cellular Automata in Fiber Arts. In: Sriraman, B. (eds) Handbook of the Mathematics of the Arts and Sciences. Springer, Cham. https://doi.org/10.1007/978-3-319-70658-0_54-2
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A Survey of Cellular Automata in Fiber Arts- Published:
- 27 August 2020
DOI: https://doi.org/10.1007/978-3-319-70658-0_54-2
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A Survey of Cellular Automata in Fiber Arts- Published:
- 13 May 2019
DOI: https://doi.org/10.1007/978-3-319-70658-0_54-1