Function with varying number of For Loops (python)

Question

My problem is difficult to explain.

I want to create a function that contains nested for loops,
the amount of which is proportional to an argument passed to the function.

Here's a hypothetical example:

Function(2)

...would involve...

for x in range (y):
    for x in range (y):
        do_whatever()

Another example...

  Function(6)

...would involve...

for x in range (y):
    for x in range (y):
        for x in range (y):
            for x in range (y):
                for x in range (y):
                    for x in range (y):
                        whatever()

The variables of the for loop (y) are NOT actually used in the nested code.

Your first thought might be to create ONE for loop, with a range that is to the power of the number argument...
THIS CAN NOT WORK because the product would be HUGE. I have instances required where there are 8 nested for loops.
The product is too large for a range in a for loop.

There are other arguments needed to be passed to the function, but I can handle that myself.

Here's the code (it creates the Snowflake Fractal)

from turtle import *
length = 800
speed(0)

def Mini(length):
    for x in range (3):
        forward(length)
        right(60)

penup()
setpos(-500, 0)
pendown()   

choice = input("Enter Complexity:")

if choice == 1:
    for x in range (3):
        forward(length)
        left(120)

elif choice == 2:
    for x in range (3):
        Mini(length/3)
        left(120)

if choice == 3:
    for x in range (6):
        Mini(length/9)
        right(60)
        Mini(length/9)
        left(120)

if choice == 4:
    for y in range (6):
        for x in range (2):
            Mini(length/27)
            right(60)
            Mini(length/27)
            left(120)
        right(180)
        for x in range (2):
            Mini(length/27)
            right(60)
            Mini(length/27)
            left(120)

if choice == 5:
    for a in range (6):
        for z in range (2):
            for y in range (2):
                for x in range (2):
                    Mini(length/81)
                    right(60)
                    Mini(length/81)
                    left(120)
                right(180)
                for x in range (2):
                    Mini(length/81)
                    right(60)
                    Mini(length/81)
                    left(120)
            right(180)
        right(180)

if choice == 6:
    for c in range (6):
        for b in range (2):
            for a in range (2):
                for z in range (2):
                    for y in range (2):
                        for x in range (2):
                            Mini(length/243)
                            right(60)
                            Mini(length/243)
                            left(120)
                        right(180)
                        for x in range (2):
                            Mini(length/243)
                            right(60)
                            Mini(length/243)
                            left(120)
                    right(180)
                right(180)
            right(180)
        right(180)

if choice == 7:
    for a in range (6):
        for b in range(2):
            for c in range (2):
                for d in range (2):
                    for e in range (2):
                        for f in range (2):
                            for y in range (2):
                                for x in range (2):
                                    Mini(length/729)
                                    right(60)
                                    Mini(length/729)
                                    left(120)
                                right(180)
                                for x in range (2):
                                    Mini(length/729)
                                    right(60)
                                    Mini(length/729)
                                    left(120)
                            right(180)
                        right(180)
                    right(180)
                right(180)
            right(180)
        right(180)

I'd appreciate any help you can give me at all,
though if you suggest a different method (such as recursion),
please don't just paste the code; instead, suggests some ideas that could put me in the right direction.

(The algorithm is for a Specialist Math Assignment)

---

specs:
Python 2.7.1
Turtle
IDLE
Windows7

Answer 1

I'm not clear why you can't use the product of the bounds and do

for x in range(y exp n)

where n is the # of loops.... You say y exp n will be huge, but I'm sure python can handle it.

However, that being said, what about some sort of recursive algorithm?

def loop_rec(y, n):
    if n >= 1:
        for x in range(y):
            loop_rec(y, n - 1)
    else:
       whatever()

Answer 2

This problem can be solved by recursion. I am just writing an algorithm here, since I believe this can be a general problem.

function Recurse (y, number) 
   if (number > 1)
      Recurse ( y, number - 1 )
   else
      for x in range (y)
      whatever()

Answer 3

Recursion will be your best bet. Consider what it should do in the base case and in the recursive case.

Code left out, as per request.

Answer 4

Here you go. Let ranges be your ranges, operate on result when you need to.

ranges=((1,4),(0,3),(3,6))
from operator import mul
operations=reduce(mul,(p[1]-p[0] for p in ranges))-1
result=[i[0] for i in ranges]
pos=len(ranges)-1
increments=0
print result
while increments < operations:
    if result[pos]==ranges[pos][1]-1:
        result[pos]=ranges[pos][0]
        pos-=1
    else:
        result[pos]+=1
        increments+=1
        pos=len(ranges)-1 #increment the innermost loop
        print result

[1, 0, 3]
[1, 0, 4]
[1, 0, 5]
[1, 1, 3]
[1, 1, 4]
[1, 1, 5]
[1, 2, 3]
[1, 2, 4]
[1, 2, 5]
[2, 0, 3]
[2, 0, 4]
[2, 0, 5]
[2, 1, 3]
[2, 1, 4]
[2, 1, 5]
[2, 2, 3]
[2, 2, 4]
[2, 2, 5]
[3, 0, 3]
[3, 0, 4]
[3, 0, 5]
[3, 1, 3]
[3, 1, 4]
[3, 1, 5]
[3, 2, 3]
[3, 2, 4]
[3, 2, 5]
[1, 0, 4]

Testing with the following would give the same result:

for x in range(*ranges[0]):
    for y in range(*ranges[1]):
        for z in range(*ranges[2]):
            print [x,y,z]