A new chaotic attractor graphics drawing method based on the curved iteration

Abstract

In this paper, we continue to study the chaotic characteristics of two curved surface mapping which forms a function in a unit area, and find that when one of the two curved surfaces is a standard curved surface and subjected to strong oscillation, and the other is randomly generate, the occurrence of chaos is more prone. Many different chaotic attractors are drawn by this method, adjusting the random surface to become subjective, the probability of chaotic attractor appearing can reach a half or more, which means that when certain conditions are meet, chaos is extremely common. Through calculating Lyapunov exponent and drawing the bifurcation diagram to analyze characteristics of chaos of the function, according to the bifurcation diagram of parameters and the Lyapunov exponent curve to look for more chaotic mapping function, a lot of chaotic attractors can be obtained. Finally a three-dimensional trigonometric function and two randomly generated three-dimensional polynomial functions are iterated, and many fancy three-dimensional attractors are obtained.