Q1: Who invented fractals/made fractals a household name / Who is Mr. Fractal?
A1: Benoit Mandelbrot. Famously known for the Mandelbrot set.

Q2: Find the corresponding eigenvectors and iterate in Maple to show that it eventually goes to 0.
A2: 
evalf((1/2)^1000*[[3], [4]] + (3/4)^1000*[[2], [3]]);
          [[              -125]  [              -125]]
          [[2.302997080 10    ], [3.454495620 10    ]]

Goes to zero!

See the attached for the calculation of the eigenvectors. I am confused by this and am needing to look into it more, but will submit attendance quiz anyways!