I enjoy expressing mathematical concepts through attributes such as color, geometric forms, and patterns. I have a background in mathematics, which provides me with a never-ending supply of subject matter, while my lifelong interest in art gives me a vocabulary and references to use in my work. Recently, I have been experimenting with geometric packing problems, particularly ones involving circles and squares. Compound packings repeat the packing process at a smaller scale and perhaps with a different shape. For example, a circle packed with circles, which are in turn packed with squares, leads to a compound packing with interesting patterns and relationships.
Artworks
Packing Squares in 23 Circles
50 x 50 cm
Archival Inkjet Print
2022
In this piece, 23 circles are optimally packed into a larger circle. The circles have radii that are proportional. If the circles are scaled so that the smallest has a radius of 1, the next biggest one will have a radius of 2, etc., with the largest one having a radius of 23. Even-numbered circles are black and odd ones are white. Squares are packed into these 23 circles according to size. For example, the 4-circle at the far right is packed with 4 white squares of the same size, while the 23-circle near the center is optimally packed with 23 black squares. These two packings are highly regular, while others are more chaotic. Small red squares denote "sliders" that occur in packing a circle that is a "rattler" in the larger circle packing.
Packing Circles in 23 Squares
50 x 50 cm
Archival Inkjet Print
2022
This work is based on a packing of 23 unequal squares into a larger square. This is one of the 12 Simple Perfect Squared Squares (SPSS) of order 23. The squares' sides can be expressed as integers with no duplicates. In this example, the square sizes vary from 1 to 79, and the outer square is size 215. Odd-numbered squares are black, evens are white. Based on their sizes, the squares are ranked from 1 to 23, and packed with that number of circles. Thus, the rank-22 square at the lower-left is packed with 22 uniform circles. One circle in this square is not held in rigidly by its neighbors and can move slightly - it is known as a “rattler.” The rattler circles in this piece are red. Squares with maximum density packings have red backgrounds.
