Week 6 Homework List

As always, a self contained ipynb solutions should be uploaded to Canvas along with a pdf copy. Each Question shall be clearly displayed inside the same notebook. Headers and formating will be graded

Question 1

For the Logistic Equation, $X_{n+1} = rX_n(1-X_n)$, find starting points and a value for $r$ that will have a periodic orbit of period 8.

Plot both the Cobweb diagram and a $X_n$ versus $ n $ graph, that clearly illustrates the periodic orbit

Question 2

Plot a subsection of the Mandelbrot set. That clearly illustrates the Fractal nature of the Set

Question 3

Plot the Julia set for $C = 0.285 + 0.01i $