Algorithmic composition with Langton’s Ant

Langton’s Ant is a simulation in two dimensions which has been proven to be a universal Turing machine – so it can in principal be used to compute anything computable by a computer.

The simulation consists of an infinite board of squares which can be either white or black. Now, an ant walks around the board. If the ant lands on a white square, it turns right, flips the color of the square and moves forward. one square If the square is black, the ant turns left, flips the color of the square and moves forward one square.

When visualised, the behaviour of this system changes over time from structured and simple to more chaotic. However, the system is completely deterministic, determined only by the starting state.

In the video above, a simulation with two ants runs over 500 steps and every time a square flips from black to white a note is played. The note to be played is determined as follows:

  • The board is divided into 7×7 sub-boards.
  • These squares are enumerated from the bottom left from 0 to 48.
  • When a square is flipped from black to white, the number assigned to the square determines the note as the number of semitones above A1.

Seven is chosen as the width of the sub-squares because it is the number of semitones in a fifth, so the ants moves either chromatically (horizontally) or in fifths (vertically). In the beginning, they are moving independently and very structured, but when their paths meet, a more complex, chaotic behaviour emerges.