# Robert Voorheis

Artist

Ypsilanti, Michigan, USA

Each of these pieces began as simple graphs that I drew during an elementary number theory course - I noticed the symmetric distribution of elements in Cayley tables for multiplicative groups of integers modulo a prime, and sketched graphs on top of them. The graphs provide a framework of simple interlocking geometric shapes onto which I can explore relationships of color and contrast.

The process of manually drawing each vertex and edge and then filling the canvas with color is deeply meditative and therapeutic. Taking the time to create these repetitive and simple objects with nothing more than my hands and rudimentary tools offers a powerful antidote for an anxious mind.

The process of manually drawing each vertex and edge and then filling the canvas with color is deeply meditative and therapeutic. Taking the time to create these repetitive and simple objects with nothing more than my hands and rudimentary tools offers a powerful antidote for an anxious mind.

p = 23, a = 1

61 x 61 cm

Acrylic on canvas

2015

This painting is given its shape by a graph which is generated by two parameters: a prime p, and an integer a, where

0 < a < p.

The vertices are the set of all integer coordinates (x, y) such that

0 < x, y < p and

x * y ≡ ±a modulo p.

Edges are chosen arbitrarily, but maintain symmetry: if an edge connects the vertices (x, y) and (u, v), then there must also be an edge connecting (-x, -y) and (-u, - v), another connecting (x, -y) and (-u, v), and another connecting (-x, y) and (u, -v).

0 < a < p.

The vertices are the set of all integer coordinates (x, y) such that

0 < x, y < p and

x * y ≡ ±a modulo p.

Edges are chosen arbitrarily, but maintain symmetry: if an edge connects the vertices (x, y) and (u, v), then there must also be an edge connecting (-x, -y) and (-u, - v), another connecting (x, -y) and (-u, v), and another connecting (-x, y) and (u, -v).

p = 41, a = 7

31 x 31 cm

Acrylic on canvas

2016

This painting is given its shape by a graph which is generated by two parameters: a prime p, and an integer a, where

0 < a < p.

The vertices are the set of all integer coordinates (x, y) such that

0 < x, y < p and

x * y ≡ ±a modulo p.

Edges are chosen arbitrarily, but maintain symmetry: if an edge connects the vertices (x, y) and (u, v), then there must also be an edge connecting (-x, -y) and (-u, - v), another connecting (x, -y) and (-u, v), and another connecting (-x, y) and (u, -v).

0 < a < p.

The vertices are the set of all integer coordinates (x, y) such that

0 < x, y < p and

x * y ≡ ±a modulo p.

Edges are chosen arbitrarily, but maintain symmetry: if an edge connects the vertices (x, y) and (u, v), then there must also be an edge connecting (-x, -y) and (-u, - v), another connecting (x, -y) and (-u, v), and another connecting (-x, y) and (u, -v).