The Pagoda Sequence: a Ramble through Linear Complexity, Number Walls, D0L Sequences, Finite State Automata, and Aperiodic Tilings

TL;DR

This paper explores the concept of number walls as an alternative to linear complexity profiles, connecting them to LFSR, D0L sequences, and aperiodic tilings, and introduces a new ternary sequence with unique properties.

Contribution

It introduces the number wall as an alternative to LCP, links it to various sequence types and tilings, and presents a new ternary sequence with deficiency 2 modulo 3.

Findings

Number wall provides an alternative to linear complexity profile.

A new ternary sequence with deficiency 2 modulo 3 is introduced.

Number wall interpreted as an aperiodic plane tiling.

Abstract

We review the concept of the number wall as an alternative to the traditional linear complexity profile (LCP), and sketch the relationship to other topics such as linear feedback shift-register (LFSR) and context-free Lindenmayer (D0L) sequences. A remarkable ternary analogue of the Thue-Morse sequence is introduced having deficiency 2 modulo 3, and this property verified via the re-interpretation of the number wall as an aperiodic plane tiling.