2023 Bridges Conference Art Exhibition

# Ulrich Reitebuch, Henriette-Sophie Lipschütz

## Artists

## Statement

Ulrich Reitebuch and Henriette Lipschütz are both mathematicians active in the field of discrete differential geometry. Next to research, they are interested in investigating connections between mathematics and the arts where they focus on geometric and symmetric structures and patterns. Next to creating illustrations digitally, both of them enjoy handcrafting examples by making them from paper, wood, thread or color.

## Artworks

The Kolakoski sequence is a self-generating integer sequence consisting solely of 1’s and 2’s, appearing either separately or in consecutive pairs. Each element is predicted by an element appearing earlier in the sequence and each element predicts elements appearing later. The diptych illustrates two conjectures for the Kolakoski sequence. The half of the diptych painted in turquois uses the guess that the frequency of 1’s equals 0.5 to distribute the elements regularly on a spiral. If a 2 predicts two 2's, one of these will again predict two 2's. Hence, there are infinite branches containing only 2’s. Whether this is true for the 1’s is unknown and illustrated in the other half - the colors indicate lengths of branches containing only 1’s.