Recursive construction of Collatz sequences tree

# Public domain code originally written by Sophie Kirschner (sophiek@pineapplemachine.com)

# constructs a tree out of possible collatz sequences
def do_steps( recursion, initial = 1 ):
    return ( initial, do_step( recursion, initial ) )
def do_step( recursion, value ):
    even = value * 2
    odd = ( value - 1 ) / 3.0
    odd = int( odd ) if odd % 2 == 1 else 0
    next_values = [ even, odd ]
    result = []
    for nvalue in next_values:
        if( nvalue > 1 ):
            next_step = do_step( recursion - 1, nvalue ) if recursion else None
            result.append( ( nvalue, next_step ) )
    return result

# output results of do_steps to the console
def output_steps( results, prefix = '' ):
    print prefix + str( results[0] ) + ':'
    if results[1]:
        for result in results[1]:
            output_steps( result, prefix + '.  ' )

# do stuff!
output_steps( do_steps( 16 ) )