A 6-Letter ‘DNA’ for Baskets with Handles†
Sculptor, Washington, DC 20002, USA
This paper is an extended version of our paper published in Mallos, J. Walking Around Trees: A 6-Letter ‘DNA’ for Baskets with Handles. In Proceedings of Bridges 2018: Mathematics, Art, Music, Architecture, Education, Culture; Torrence, E.T.B., Séquin, C., Fenyvesi, K., Eds.; Tessellations Publishing: Phoenix, AZ, USA, 2018; pp. 219–224.
Received: 12 December 2018 / Revised: 1 February 2019 / Accepted: 3 February 2019 / Published: 13 February 2019
Fabric surfaces, made using techniques such as crochet and net-making, are typically worked in a linear order that meanders, without crossing itself, to ultimately visit and build the entire surface. For a closed basket, whose surface is a topological sphere, it is known that the construction can be described by a codeword on a 4-letter alphabet via Mullin’s encoding of plane graphs. Mullin’s code exemplifies the formal language known as the Shuffled Dyck Language with 2 Types of Parenthesis (
). Besides its 4-letter alphabet,
has some other similarities to DNA: Any word can be ‘evolved’ via a sequence of local mutations (rewriting rules), and ‘gene-splicing’ two
words, by an insertion or concatenation, produces another
comes up short when we attempt to make a basket with handles. I show that extending the language to
, by addition of a third type of parenthesis, succeeds for orientable surfaces with handles—provided an appropriate choice of cut graph is made.
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MDPI and ACS Style
Mallos, J. A 6-Letter ‘DNA’ for Baskets with Handles. Mathematics 2019, 7, 165.
Mallos J. A 6-Letter ‘DNA’ for Baskets with Handles. Mathematics. 2019; 7(2):165.
Mallos, James. 2019. "A 6-Letter ‘DNA’ for Baskets with Handles." Mathematics 7, no. 2: 165.
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