Homework 6: Analyzing the Fractal Characteristics of the Henon Map, Assignments of Physics

Download Homework 6: Analyzing the Fractal Characteristics of the Henon Map and more Assignments Physics in PDF only on Docsity! Homework 6 Due: Thursday 12 October In this homework you will investigate another discrete time nonlinear dy- namics – the Henon map. It is similar to the Sierpinski map as it involves two dynamical variables x and y. The update equation is x n+1 = yn + 1 − ax 2 n y n+1 = bxn For this homework we will take a = 1.4 and b = 0.3 1. Modify the Sierpinski code you worked with in lab 6 to implement the Henon dynamics. Include your modified code in your writeup. 2. The Henon map for these parameter values exhibits chaos. Show that the strange attractor has fractal characteristics (you may want to in- clude snapshots of pieces of the attractor at different magnifications) 3. Calculate, using your code, the (box counting) fractal dimension of the Henon map. 1