Revolving sequences and Terdragon

TL;DR

This paper extends the concept of revolving sequences to include a broader class of self-similar fractals, notably introducing a new type that parametrizes the Terdragon and other fractals within Iterated Function Systems.

Contribution

It generalizes revolving sequences to encompass more fractals, including the Terdragon, expanding their applicability in parametrizing self-similar fractals.

Findings

Introduced a new type of revolving sequence.

Parametrized the Terdragon fractal.

Extended the framework to more Iterated Function Systems.

Abstract

In 1970, Davis and Knuth introduced the concept of revolving sequences to represent Gaussian integers. Much later, Kawamura and Allen recently generalized this idea to a wider class of revolving sequences that parametrize certain self-similar fractals including the Levy Dragon and Tiling Dragon, which are the unique compact solution of certain families of Iterated Function Systems. In this paper, we build on the work of Kawamura and Allen to include a wider collection of Iterated Function Systems and introduce a new type of revolving sequence which parametrizes a different family of self-similar fractals including the Terdragon.