English: Directed graph showing the orbits of the odd numbers less than 50 (with the exceptions of 27, 31, 41, and 47, because they would make it too tall) under the Collatz map.

For a larger graph, see :Image:Collatz-graph-300.svg.

Created with Graphviz, with the help of this Python program:

 dotfile = file('collatz-graph.dot', 'w')
 
 limit = 50
 
 def f(n):
   while n % 2 == 0: # divide by 2 until it's odd
     n /= 2
   n = 3*n + 1
   while n % 2 == 0:
     n /= 2
   return n
 
 explored = set([1,27,31,41,47])
 
 dotfile.write('digraph {\n')
 
 for n in range(3, limit, 2): # odd numbers
   while n not in explored:
     dotfile.write(str(n) + ' -> ')
     explored.add(n)
     n = f(n)
   dotfile.write(str(n) + ';\n')
 
 dotfile.write('}\n')