Visualisation of the Kolakoski sequence (Henriette-Sophie Lipschütz, Ulrich Reitebuch, Mathart 2022) скачать в хорошем качестве

Visualisation of the Kolakoski sequence (Henriette-Sophie Lipschütz, Ulrich Reitebuch, Mathart 2022)

The OEIS defines the self-describing Kolakoski sequence (A000002) by listing the number of consecutive repetitions of an element. It consists of 1’s and 2’s only and starts with 1. Both, 1 and 2, occur in a sequence of equal elements of either one or two consecutive terms. A common way to depict this sequence consists of distributing the elements on a spiral. Based on the conjecture that the share of 1’s corresponds to the share of 2’s, the elements are distributed such that the angle density of the elements on the spiral increases exponentially. Next to the consecutive elements on the spiral, each element is related to another element which already appeared on the spiral. This element predicts the repetition of the considered one. Depending on whether the considered element is a 1 or a 2, it is connected to the one or two elements it predicts. By connecting each 1 to the predicted element occuring on the next winding by a straight line segment and each 2 to the two predicted elements by straight line segments, resulting locally in a Y shape, this procedure results in a tree-like fractal structure in the plane. -- Talk by Henriette-Sophie Lipschütz and Ulrich Reitebuch (both Freie Universität Berlin) -- Talk given at: Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 12. - 16. September 2022 (https://ms-math-computer.science/proj...) Organized by: Milena Damrau and Martin Skrodzki (https://ms-math-computer.science/) Twitter:   / msmathcomp   -- See also: Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 14-17 September 2020 (https://ms-math-computer.science/proj...) Playlist:    • DMV Minisymposium "Mathematics and Arts" 2020   Minisymposium "Mathematics and Arts" at the annual meeting of the German Mathematical Society, 27 September - 1 October 2021 (https://ms-math-computer.science/proj...) Playlist:    • Jigsaw puzzles, bell ringing, and Hamilton...