New Classes of Regular Symmetric Fractals

The paper introduces new fractal families many of which approach optimal information dimension for annular and checkerboard structures and include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined, and a notation to represent the families is proposed....

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Bibliographic Details
Published inCircuits, systems, and signal processing Vol. 41; no. 7; pp. 4149 - 4159
Main Author Kak, Subhash
Format Journal Article
LanguageEnglish
Published New York Springer US 01.07.2022
Springer Nature B.V
Subjects
Circuits and Systems
Electrical Engineering
Electronics and Microelectronics
Engineering
Fractals
Instrumentation
Mapping
Self-similarity
Short Paper
Signal processing
Signal,Image and Speech Processing
Optimal dimensionality
Fractal data
Noninteger dimensions
Information theory
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Summary:The paper introduces new fractal families many of which approach optimal information dimension for annular and checkerboard structures and include the Sierpinski carpet and the Menger sponge as special cases. The complementary mapping is defined, and a notation to represent the families is proposed. The new classes represent an enhanced set that goes beyond the recently published results on optimal information dimensionality and they can be expected to have applications in natural and engineered self-similar systems.
ISSN:0278-081X
1531-5878
DOI:10.1007/s00034-022-01966-z