File:Collatz-graph-all-30-no27.svg
يمكن اعتبار المشكلة التي يثيرها هي مشكلة رياضية غير محلولة بعد وقد سميت باسم Lothar Collatz الذي اكتشفها عام 1937 م.
Summary
Directed graph showing the orbits of the numbers less than 30 (with the exception of 27 because it would make it too tall) under the Collatz map.
For a larger graph containing only odd numbers, see Image:Collatz-graph-300.svg.
Created with Graphviz, with the help of this Python program:
dotfile = file('collatz-graph.dot', 'w')
limit = 30
def f(n):
if n % 2 == 0:
return n / 2
else:
return 3*n + 1
explored = set([1,27]) # 27 has a long convergence, so skip it
dotfile.write('digraph {\n')
for n in range(2, limit):
while n not in explored:
dotfile.write(str(n) + ' -> ')
explored.add(n)
n = f(n)
dotfile.write(str(n) + ';\n')
dotfile.write('}\n')
enSVG development
Category:Valid SVG created with Graphviz code:Diagrams#Collatz-graph-all-30-no27.svg
Category:Translation possible - SVGThis diagram uses embedded text that can be easily translated using a text editor.
Source code
Graphviz mscgen code
dotfile = file('collatz-graph.dot', 'w')
limit = 30
def f(n):
if n % 2 == 0:
return n / 2
else:
return 3*n + 1
explored = set([1,27]) # 27 has a long convergence, so skip it
dotfile.write('digraph {\n')
for n in range(2, limit):
while n not in explored:
dotfile.write(str(n) + ' -> ')
explored.add(n)
n = f(n)
dotfile.write(str(n) + ';\n')
dotfile.write('}\n')
Licensing
 |
This work has been released into the public domain by its author, Keenan Pepper. This applies worldwide. In some countries this may not be legally possible; if so: Keenan Pepper grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
