The Ibaguner Fractal Operator (IFO): Hyperbolic Truncuoid Generalization of Conic Pythagorean Structure

Key Points

• The aim is to develop the Ibaguner Fractal Operator (IFO) as a generalization of the conic Pythagorean structure for advanced geometrical analysis.
• Developed the Ibaguner Fractal Operator using hyperbolic and exponential concepts.
• Replaced trigonometric generators with hyperbolic generators and exponential lifting.
• Constructed a mixed curvature decomposition with axial growth and a rotational phase channel.
• Introduced a hyperbolic truncuoid envelope geometry as opposed to classical conic surfaces.
• Established a hyperbolic logarithmic operator norm form.
• Demonstrated fractal scaling behavior within the mixed curvature structure.

Abstract