Another excellent video from Veritasium. Starts with the logistic equation and through a series of very clear examples gets to the relationship between growth rate (r) and equilibrium population. He does go into how this graph relates to the Mandelbrot set, but the rotating graphs are a little tricky to follow. However, the discussion of the practical applications of chaos theory (at 10:35) is really nice as well.
Note:
The logistic equation:
gives the new population (xₙ₊₁) for a given growth rate (r) and the old population (xₙ).
This makes for a fairly nice and easy programming assignment.