Extending Chaos through Real-Number Iterations of Functions Using Fuzzy Concepts

What is it about?

This work focuses on a mathematical concept called Iterated Function Systems (IFS), which traditionally involve applying a function repeatedly a whole number of times (like once, twice, or three times). However, this study introduces a new idea: instead of limiting to whole numbers, the function can be Iterated a fractional or real number of times (e.g., 1.5 times or √2 times).

Featured Image

Photo by Tim Johnson on Unsplash

Photo by Tim Johnson on Unsplash

Why is it important?

Real-number iterations could have practical implications in areas like control systems, signal processing, or any field involving dynamics. This new framework might lead to better models and solutions for complex problems.

Perspectives

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When the idea of real-number iterations came to mind, it felt like a moment of relief following a surge of curiosity. As a PhD student, the journey is often marked by more stress than the joy of discovery. However, I hope this new concept will pave the way for more versatile and insightful studies in the fields of dynamics and Iterated Function Systems (IFS).

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