Rachel A H Beckett
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.
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.