The Continued Fraction Structure in Physical Fractal Theory

Abstract

The objective of this study is to reveal the intrinsic connection between fractal operators in physical fractal spaces and continued fractions. The specific contributions include: (1) reviewing fundamental concepts of continued fractions and physical fractal theory; (2) establishing algebraic structure consistency between continued fractions and fractal operators through the medium of generation mappings; (3) discussing the convergence of fractal operators by employing theory from continued fraction analysis; and (4) confirming the correspondence between fixed points of infinite continued fractions and algebraic equations governing fractal operators.

Keywords

• physical fractal theory
• fractal operator
• continued fraction
• fixed point