Geodesic
Colorings of Plane Patterns Defined by Sequences and Arrays, Inspired by Weaving Designs
This article describes schemes for coloring an $m \times n$ grid in two or more colors. Such a grid is based on the ``product'' of two q-ary sequences, one of length m and the other of length n, each built from an alphabet A containing q distinct symbols and a $q \times q$ product matrix that defines the product of two elements a_i and a_j of A. With this product matrix and a color set containing up to q^2 colors, we define the $m \times n$ product of two such q-ary sequences, along with its associated $m \times n$ colored grid. Considered in detail is the special case when the product matrix is a one-step left (or right) circulant latin square and the number of colors is from 2 to q, as results when the operation is addition (or subtraction) with modular arithmetic.
Classification : 20H15 
@article{VM_2011_13_2_a2,
     author = {Shelley L. Rasmussen},
     title = {Colorings of {Plane} {Patterns} {Defined} by {Sequences} and {Arrays,} {Inspired} by {Weaving} {Designs}},
     journal = {Visual Mathematics},
     publisher = {mathdoc},
     volume = {13},
     number = {2},
     year = {2011},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/VM_2011_13_2_a2/}
}
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Shelley L. Rasmussen. Colorings of Plane Patterns Defined by Sequences and Arrays, Inspired by Weaving Designs. Visual Mathematics, Tome 13 (2011) no. 2. http://geodesic.mathdoc.fr/item/VM_2011_13_2_a2/