Playing with my son Federico

graph.png

graph.py

from collections import deque
from subprocess import Popen, PIPE
from sys import argv

first, last = map(int, argv[1:3])
name = argv[3]

ops = [
    lambda x: x + 1,
    lambda x: x * 2
]

frontier = deque([first])
seen = set()
graph = 'graph G {\nnode [shape=point]'
while frontier:
    v = frontier.popleft()
    if v in seen: continue
    for op in ops:
        u = op(v)
        if u > last: continue
        graph += '\t{} -- {}'.format(v, u)
        frontier.append(u)
    seen.add(v)
graph += '}'

sfdp = Popen(['sfdp', '-Tpng'], stdin = PIPE, stdout = PIPE)
with open('{}.png'.format(name), 'wb') as of:
    of.write(sfdp.communicate(input = graph)[0])

This is the script used to generate the above PNG, that also appears in this tweet; it is based on Graphviz and assumes sfdp layout tool of such package to be in the path.

The tool generates a graph G=(V, E) such that V = {first <= x <= last} and E = {(x, y) : y = x + 1} U {(x, y) : y = 2x}

To run it, just pass the first and last number to consider and the basename of the graph, as in

python graph.py 1 10000 graph

and open  graph.png.

Just works on python 2.7. And here it produces really small images, like 179x173 with the args 1 10000. Any idea why?

I guess you mean 179x173 pixels, the image size depends on the sfdp tool, part of Graphviz. You can check the manual to see if you can specify a larger size, this Stack Overflow answer could be a good starting point.