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.
Highlights
∗Address: Department of Mathematics, University of North Texas, 1155 Union Circle #311430, Denton, TX 76203-5017, USA; E-mail: kiko.kawamura@unt.edu, andrew.allen@unt.edu. They showed that each Gaussian integer has exactly four representations of this type: one each in which the right-most non-zero value takes on the values 1, −1, i, −i
Is there a generalized relationship between sets of revolving sequences and self-similar sets? In particular, we are interested in describing selfsimilar sets which arise from more general revolving sequences, where the 90 degree angle of rotation is replaced with a more general angle
Theorem 1.2 shows a direct relationship between generalized revolving sequences and self-similar sets generated by the iterated function system (IFS) from (1.1): ψ1(z) = αz, ψ2(z) =z + α
Summary
Δn) such that n z = δn−k(1 + i)k, k=0 where δk ∈ {0, 1, −1, i, −i} with the restriction that the non-zero values must follow the cyclic pattern from left to right:. Levy’s curve and Dragon are very different: one is a continuous curve while the other is a tiling fractal; both are self-similar sets. We are interested in describing selfsimilar sets which arise from more general revolving sequences, where the 90 degree angle of rotation is replaced with a more general angle Is there a generalized relationship between sets of revolving sequences and self-similar sets? In particular, we are interested in describing selfsimilar sets which arise from more general revolving sequences, where the 90 degree angle of rotation is replaced with a more general angle
Sign-in/Register to view highlights & summary Sign-in/Register to access full text options 
Talk to us
Join us for a 30 min session where you can share your feedback and ask us any queries you have
Schedule a callMore From: Journal of Fractal Geometry, Mathematics of Fractals and Related Topics
Disclaimer: All third-party content on this website/platform is and will remain the property of their respective owners and is provided on "as is" basis without any warranties, express or implied. Use of third-party content does not indicate any affiliation, sponsorship with or endorsement by them. Any references to third-party content is to identify the corresponding services and shall be considered fair use under The CopyrightLaw.
