2023 Joint Mathematics Meetings
Rachel A H Beckett
Artists
Rachel A H Beckett
Artist
Alumna, University of Cambridge
Stroud, Gloucestershire, UK
Statement
This project explores the most efficient way of packing unit circles into a larger enclosing circle. I had used circle packing in my art on several occasions before it occurred to me that it would be interesting to find the series of diameters of the smallest circles that could contain n circles, starting with n = 1. I first tried this intuitively, then compared my results online with the optimal ones that have been proven up to 13. After number 8, several of my results differed - an interesting demonstration of the limitations of intuition. This artwork shows the proven optimal packings of the first 13 integers.
Artworks
The optimal packings of the first 13 integers spiral out from the center. Each circle evolves from the last. Note the diameters of 6 and 7 are the same. I have assumed a vertical line of symmetry and a top and a bottom, rather like the zoning controlled by hox genes in organism growth (except in 12 which is flower-like). I have built up the patterns from chains of circles, linked by 'weak bonds'. A new chain has a new color. When a chain gains a disk it remains the same color. When broken and reformed it assumes the color of the host chain.
The disc decoration shows hexagonal tessellation: the lattice for optimal packing of circles in a plane. The colours reflect my aesthetic preferences and synaesthetic association of colors with numbers.