A Survey of Cellular Automata in Fiber Arts
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 aut
- PDF / 2,017,968 Bytes
- 23 Pages / 439.36 x 666.15 pts Page_size
- 80 Downloads / 184 Views
Contents Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Representations of Cellular Automata in Fiber Arts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Sierpi´nski Triangles and Related Cellular Automata . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Other Designs from Well-Known Cellular Automata Rules . . . . . . . . . . . . . . . . . . . . . . . . . . Cellular Automata Designs Created for Fiber Arts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . Cross-References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2 2 10 10 15 18 22 22 22
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.
J. Holden () Rose-Hulman Institute of Technology, Terre Haute, IN, USA e-mail: [email protected] L. Holden SkewLoose, LLC, Terre Haute, IN, USA e-mail: [email protected] © Springer Nature Switzerland AG 2020 B. Sriraman (ed.), Handbook of the Mathematics of the Arts and Sciences, https://doi.org/10.1007/978-3-319-70658-0_54-2
1
2
J. Holden and L. Holden
Keywords Cellular automata · Fiber arts · Game of Life · Elementary cellular automata · Sierpi´nski triangle · Knitting · Crochet · Weaving · Cross-stitch · Beading
Introduction Mathematicians in general are intensely creative people and often express themselves in art. Conversely, artists frequently explore the constraints of structure in their work, and mathematics is a common way to do that. The intersection of artistic creativity and mathematical structure can be particularly fruitful when the mathematics is easy to work with and yet produces complex results. At the same time, the choice of artistic medium can be chosen to either support or work against the structure. Cellular automata were first explored in the 1940s in order to conceptualize the idea of a programmable machine in the simplest possible
Data Loading...
