File:Collatz-graph-all-30-no27.svg
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![File:Collatz-graph-all-30-no27.svg](https://upload.wikimedia.org/wikipedia/commons/thumb/a/ad/Collatz-graph-all-30-no27.svg/72px-Collatz-graph-all-30-no27.svg.png?20070610225558)
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يمكن اعتبار المشكلة التي يثيرها هي مشكلة رياضية غير محلولة بعد وقد سميت باسم Lothar Collatz الذي اكتشفها عام 1937 م.
Summary
[edit]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')
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![](https://upload.wikimedia.org/wikipedia/commons/thumb/2/21/Beziehung_Graphviz.svg/15px-Beziehung_Graphviz.svg.png)
This diagram was created with Graphviz.
![](https://upload.wikimedia.org/wikipedia/commons/thumb/9/99/OOjs_UI_icon_language-constructive.svg/22px-OOjs_UI_icon_language-constructive.svg.png)
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Source code
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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
[edit]Public domainPublic domainfalsefalse |
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This work has been released into the public domain by its author, I, Keenan Pepper. This applies worldwide. In some countries this may not be legally possible; if so: I, Keenan Pepper grants anyone the right to use this work for any purpose, without any conditions, unless such conditions are required by law. |
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Date/Time | Thumbnail | Dimensions | User | Comment | |
---|---|---|---|---|---|
current | 22:55, 10 June 2007 | ![]() | 258 × 2,125 (20 KB) | Keenan Pepper (talk | contribs) | 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.sv |
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