About the Quilts
The quilts are made using Cayley tables as a basic pattern which is repeatedly tiled
across the quilt surface. The tables show the results of combining elements in a set using
various operations. For a familiar example of how Cayley tables can be constructed using Clock Arithmetic,
click over to the Clock Arithmetic demonstration.
These tables often produce symmetrical patterns which illustrate the sets' mathematical properties.
In the quilt tables, painted tiles take the place of the sets' elements.
The following tables can be made :
Addition mod n
Multiplication mod n
Dihedral groups D3 and D4
Direct sums Z2+Z2, Z2+Z2+Z2 and Z2+Z3
Quaternion group Q8
The quilt is tiled using one of the following patterns :
Reflection
The four quadrants of the quilt are tiled clockwise with
vertical and horizontal reflections of the original table.
Rotation
The four quadrants of the quilt are tiled clockwise with
four successive 90 degree clockwise rotations of the original table.
Fibonacci
The quilt is tiled with 64 tables spaced and sized according to the
first numbers of the fibonacci sequence. The four quadrants are also reflected.
D4 Table
The D4 Table quilt is a Cayley table for the dihedral group D4,
whose motions are applied to the image of the original table.
Golden Rectangle
The is a reflection quilt whose quadrants contain golden
rectangles constructed from the original table using recursive subdivision :
each golden rectangle is divided into a square and a smaller golden rectangle
(which is in turn subdivided). Each subdivided region then has the image of the
table stretched over it.
Color Addition
A reflection quilt whose quadrants contain color-shifted copies
of the table. The color of each pixel in the image of the table is increased
by the sum of its x and y coordinates modulo n, where n is the size of the table's image
in pixels.
Parallelogram
The table is shaped into a parallelogram which wraps around
the table's original square, then it is reflected onto the quilt.
This applet is based on ideas from original papers by Forseth & Troutman. See, for example,
Forseth, S; Troutman, A. "Designs Exhibiting Mathematical Structure,"
School Science and Mathematics, Volume 74, December 1974.