One simple improvement to the code I gave in Assignment 8 would be to define the function as below. In this way, f actually takes input which is an ordered pair (c,x), and outputs another ordered pair (c, x^2 + c). Then when building the long term values list, we get somewhat simpler code.

gistfile1.py

def f((c,x)):
    return (c,x^2 + c)

def LTV(c):
    "returns last 50 results from iterating f 500 times beginning with (c,0)"
    points=[(c,0)]
    for i in range(500):
        newpoint = f(points[-1]) 
        points.append(newpoint)
    return points[-50:]

def LTVInterval(a,b):
    "returns long term vals for 1000 choices of c between a and b"
    data=[]
    for i in range(1000):
        c = a + i*(b-a)/1000
        data.extend(LTV(c))
    return data