×

On formal descriptions for knitting recursive patterns. (English) Zbl 1151.68734

Summary: We investigate relationships between knitting and formal systems. We show how formal languages, grammars, and algorithms give rise to powerful tools that can be used in both descriptive and prescriptive ways that have not yet been fully explored for designing, then knitting, complex patterns. In particular, we generate knitting meta charts, i.e. abstract schemes, which admit different knitting charts according to the knitting techniques chosen. We thus produce new intricate and recursive patterns which in our opinion also exhibit a sense of artistry and beauty.

MSC:

68W05 Nonnumerical algorithms
00A66 Mathematics and visual arts
68Q30 Algorithmic information theory (Kolmogorov complexity, etc.)
68Q42 Grammars and rewriting systems
PDFBibTeX XMLCite
Full Text: DOI

References:

[1] Allen P, Knitting for Dummies (2002)
[2] Bernasconi, A, Bodei, C and Pagli, L. Knitting for fun: a recursive sweater. Proceedings of Fun with Algorithms, 4th International Conference, FUN 2007. Castiglioncello, Italy. pp.53–65. Berlin: Springer. Lecture Notes in Computer Science 4475 · Zbl 1201.68145
[3] Cormen TH, Introduction to Algorithms, 2. ed. (2001)
[4] DOI: 10.1016/S0304-3975(00)00168-7 · Zbl 0949.68148 · doi:10.1016/S0304-3975(00)00168-7
[5] Drewes, F and Klempien-Hinrichs, R. Picking knots from trees–the syntactic structure of celtic knotwork. Proceedings of the First International Conference, Diagrams 2000. Edinburgh, Scotland, UK. pp.89–104. Heidelberg: Springer-Verlag. Lecture Notes in Computer Science 1889 · Zbl 0973.68240
[6] Drewes F, Proceedings of Developments in Language Theory (DLT ’99) pp 326– (1999)
[7] New D, Unexpected knitting (2007)
[8] Ekart, A. Genetic programming for the design of lace knitting stitch patterns. Proceedings of Genetic and Evolutionary Computation Conference (GECCO). London, United Kingdom, Bremen, Germany. pp.2457–2461. New York, USA: ACM. Lecture Notes in Computer Science 2278
[9] Habel, A and Kreowski, HJ. Collage grammars. Proceedings of Graph-Grammars and Their Application to Computer Science. pp.411–429. Berlin: Springer. Lecture Notes in Computer Science 532 · Zbl 0768.68081
[10] Hopcroft JE, Introduction to Automata Theory, Languages, and Computation, 3. ed. (2007)
[11] Leighton FT, Parallel Algorithms and Architectures: Array, Trees, Hypercubes (1992)
[12] Li M, An Introduction to Kolmogorov Complexity and Its Applications (2005)
[13] DOI: 10.1016/S0019-9958(73)80004-X · Zbl 0273.68055 · doi:10.1016/S0019-9958(73)80004-X
[14] Schmidhuber J, J. Int. Soci. Arts, Sci. Tech. 30 pp 97– (1997)
[15] Suzuki, D. A supporting system for colored knitting design. Proceedings of the 13th International Conference on Industrial and engineering applications of artificial intelligence and expert systems, IEA/AIE. New Orleans, Louisiana, USA. Berlin: Springer-Verlag. Lecture Notes in Computer Science 1821
This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. In some cases that data have been complemented/enhanced by data from zbMATH Open. This attempts to reflect the references listed in the original paper as accurately as possible without claiming completeness or a perfect matching.