2018 Joint Mathematics Meetings

# Vincent J. Matsko

## Artists

## Statement

Work in this exhibition is based on fractal binary trees. The usual way of creating a binary tree is to move forward, then branch to the left and right some fixed angle as well as shrink, and repeat recursively. Recent work involves specifying the branching by arbitrary affine transformations. In these two pieces, the affine transformations were chosen so that as the tree grows, nodes are repeatedly visited. The nodes are covered by disks which become smaller with each iteration, accounting for the overlapping circles. The research needed to produce these images was undertaken jointly with Nick Mendler.

## Artworks

In this piece, nodes are revisited every three iterations. The first branching transformation was a slight rotation and shrink followed by a translation, and the second affine transformation was calculated to force the revisiting of nodes. The color palette was chosen to reflect the similarity of the pattern of nodes to images of stars in galaxies.

In this piece, nodes are revisited every three iterations. The first branching transformation is just a 120 degree rotation, which produces the equilateral triangles consisting of the gray branches. The second is a 120 degree rotation in the opposite direction, combined with a shrink. The result is an image which resembles a Sierpinski triangle.