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Local -fractal interpolation function
Akash Banerjee1, Md Nasim Akhtar1,2, M A Navascués1
1Department of Mathematics, Presidency University, 86/1, College Street, Kolkata, 700 073 India.
The European Physical Journal. Special Topics
|June 26, 2023
Summary
This study introduces local non-affine fractal functions, extending traditional fractal interpolation. A new fractal operator is defined to map classical functions to their local fractal counterparts.
Area of Science:
- Mathematics
- Fractal Geometry
- Functional Analysis
Background:
- Global fractal interpolation functions have been extensively studied.
- Local fractal functions, based on local iterated function systems, generalize traditional fractal systems.
Purpose of the Study:
- To construct local non-affine fractal functions.
- To define and study properties of a fractal operator that maps classical functions to local fractal counterparts.
Main Methods:
- Construction of local non-affine fractal functions.
- Definition of a fractal operator.
- Analysis of the fractal operator's properties.
Main Results:
- Successfully constructed local non-affine fractal functions.
- Defined a novel fractal operator.
- Provided illustrative examples of the constructed functions' graphs.
Conclusions:
- The study successfully extends fractal interpolation to local non-affine fractal functions.
- The introduced fractal operator provides a bridge between classical and local fractal function spaces.
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