Chaotic Behavior of the Folding Map on the Equilateral Triangle

Abstract

In recent years, it becomes important to understand chaotic behaviors in order to analyze nonlinear dynamics because chaotic behavior can be observed in many models in the field of physics, biology, and so on. To understand chaotic behaviors, investigating mechanisms of chaos is necessary and it is meaningful to study simple models that shows chaotic behaviors. In this paper, we propose an extremely simple triangle folding map and show that the map has k -periodic points for any integer k , and show the map has sensitivity to initial conditions. Finally, we discuss the connection with the Sierpinski gasket and construct similar types of fractal geometry.