Choose one of the following to answer: a) Describe the Mandelbrot set by discussing the difference in the points in the 'inside' points, points close to the boarder, and points further out from the boarder. Write a brief algorithm of how you would code a program like the one in the video 'whats so special about the Mandelbrot Set' in week 4 topic introduction. b) Construct a variation of the Recaman sequence numerically and also with a picture and formula. This variation is that you do not increase by one, but by even numbers. Thus move up or back 2, then 4, then 6, etc. c) It is expected in traditional mathematics that when you input data into a well-defined equation you get an expected output. We looked at the logistic equation f(x) = rx(1-x) with different initial inputs. Explain how with some initial conditions, we get a predictable result but with others the result was surprisingly different - how was it different?