# Revolving Fractals

## TL;DR

This paper generalizes the concept of revolving sequences related to Gaussian integers, connecting them to self-similar sets like the Dragon, and introduces a new parametrized expression for these fractals.

## Contribution

It extends previous work on revolving sequences, providing a generalized framework and a new parametrized formula for specific self-similar fractal sets.

## Key findings

- Established a generalized relation between revolving sequences and self-similar sets.
- Derived a new parametrized expression for certain fractals.
- Connected revolving sequences to the structure of the Dragon fractal.

## Abstract

Davis and Knuth in 1970 introduced the notion of revolving sequences, as representations of a Gaussian integer. Later, Mizutani and Ito pointed out a close relationship between a set of points determined by all revolving sequences and a self-similar set, which is called the Dragon. We will show how their result can be generalized, giving a new parametrized expression for certain self-similar sets.