Play with the differences between linear values, quadratic values, exponential values, and whatever else you like.

arithmetic-diff.py

DEPTH = 6
LENGTH = 12

#Change me!
def f(i):
    return i
    #also try:
    #return i**2
    #return 2**i

vals = [[f(i) for i in range(1,LENGTH)]]
for i in range(DEPTH):
    old = vals[-1]
    current = []
    for j in range(len(old)-1):
        current.append(old[j+1]-old[j])
    vals.append(current)

for level in range(len(vals)):
    if len(vals[level]) == 0:
        break
    print level*"      ",
    for x in vals[level]:
        outstr = '%+g' % round(x,3)
        print outstr + (6-len(outstr))*" "+ "     ",
    print