Ex. 1 → Write a function that plots an ellipse given its center coordinates (x,y), the half axis a and b rotation angle θ.

Ex. 2 → Write a short program that takes a 2D array, e.g., the preceding Mandelbrot contour image, and iteratively replace each value by the average of its neighbors. Update a contour plot of the array in a figure window to animate the evolution of the contours. Explain the behavior.

Ex. 3 → Consider an N × N matrix or image with integer values. The mapping

is an example of a mapping of a toroidal square grid of points onto itself. This has the interesting property that it distorts the image by shearing and then moving the pieces outside the image back using the modulu function mod. Applied iteratively, this results in randomizing the image in a way that eventually returns the original. Implement the following sequence:

and save out the first N steps to files or plot them in a figure window.

As an example image, you can use the classic 512 × 512 Lena test...