Fractals corresponding to the metallic means sequences
Y. S. J. Liang, Darren C. Ong
TL;DR
This paper introduces a new class of fractals based on metallic means sequences, providing formulas for their fractal dimensions, thus linking number theory and fractal geometry.
Contribution
It presents a novel construction of fractals associated with metallic means sequences and derives explicit formulas for their fractal dimensions.
Findings
Fractals are constructed from metallic means sequences.
Explicit formulas for fractal dimensions are obtained.
The work bridges number theory and fractal geometry.
Abstract
In this work, we introduce a class of fractal subsets of corresponding to the aperiodically ordered metallic means sequences. We find simple formulas for the fractal dimension for these fractals.
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Taxonomy
TopicsAdvanced Mathematical Theories and Applications