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Related Experiment Video

Updated: Jan 24, 2026

Generating a Fractal Microstructure of Laminin-111 to Signal to Cells

Generating a Fractal Microstructure of Laminin-111 to Signal to Cells

Published on: September 28, 2020

Generation of fractals as Duffing equation orbits.

Marat Akhmet¹, Mehmet Onur Fen², Ejaily Milad Alejaily¹

¹Department of Mathematics, Middle East Technical University, 06800 Ankara, Turkey.

Chaos (Woodbury, N.Y.)

|June 4, 2019

Summary

This study introduces dynamics for fractals using the Duffing equation and Fatou-Julia iterations. This approach characterizes fractals as trajectory points, enhancing understanding of chaos and fractal geometry.

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Area of Science:

Complex Systems
Dynamical Systems Theory
Fractal Geometry

Background:

Fractals exhibit complex geometric properties.
The Duffing equation is a well-known model in nonlinear dynamics.
Fatou-Julia iterations are fundamental in complex dynamics.

Purpose of the Study:

To construct dynamics for fractals.
To establish a criterion for fractal mapping.
To link fractal geometry with dynamical systems and chaos theory.

Main Methods:

Utilizing the motion associated with the Duffing equation.
Developing iterations based on the Fatou-Julia paradigm.
Mapping fractals and ensuring the resulting image remains fractal.

Main Results:

Successfully constructed dynamics for fractals.
Developed a criterion to maintain fractal properties under iteration.
Characterized fractals as points on solution trajectories of differential equations.

Conclusions:

The study establishes a novel method for introducing dynamics to fractals.
This work deepens the understanding of the relationship between chaos and fractal geometry.
The findings have potential applications in physics and engineering.