In this worksheet we'll explore creating the tree from the 3n+1 conjecture.
A graph is a dictionary containing pairs: v: L where v is a vertex, and L is a list of vertices adjacent to v
d = {0: [1,4,5], 1: [2,6], 2: [3,7], 3: [4,8], 4: [9], 5: [7, 8], 6: [8,9], 7: [9]}
G = Graph(d)
plot(G)
show(G)
G=Graph(d)
G
CollatzTree={}
for i in srange(2,10):
if i%3==1:
CollatzTree.update({i:[(i-1)/3,2*i]})
else:
CollatzTree.update({i:[2*i]})
print(CollatzTree)
{2: [4], 3: [6], 4: [1, 8], 5: [10], 6: [12], 7: [2, 14], 8: [16], 9:
[18]}
CollatzTree.update({16:[5,8]})
CollatzTree.update( {3:[6,10] })
CollatzTree.update( {9:[18,28] })
CollatzTree.update({14:[28]})
T=Graph(CollatzTree)
from sage.graphs.graph_plot import GraphPlot
T.show(layout='tree', tree_root=1)
T.is_tree()
True
show(T)
CollatzTree={}
for i in srange(1,27):
a=i
while a>1:
if is_even(a):
#if a<50:
CollatzTree.update({a:[a/2]})
a=a/2
else:
#if a<50:
CollatzTree.update({a:[3*a+1]})
a=3*a+1
T=Graph(CollatzTree)
show(T)
x=T.graphplot(layout='tree', tree_root=1,tree_orientation='up')
x.show(figsize=[25,20])
sage.graphs.graph_plot.DEFAULT_SHOW_OPTIONS['figsize'] = [10,10]
plot(x,figsize=[8,8])
Traceback (click to the left of this block for traceback) ... TypeError: eval() got multiple values for keyword argument 'locals' Traceback (most recent call last):
File "", line 1, in <module>
File "/usr/local/sage-6.10/local/lib/python2.7/site-packages/sagenb-0.11.4-py2.7.egg/sagenb/misc/support.py", line 438, in syseval
return system.eval(cmd, sage_globals, locals = sage_globals)
File "/usr/local/sage-6.10/local/lib/python2.7/site-packages/sage/misc/html.py", line 82, in wrapped
output = method(*args, **kwds)
TypeError: eval() got multiple values for keyword argument 'locals'
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{2: [4], 3: [6], 4: [1, 8], 5: [10], 6: [12], 7: [2, 14], 8: [16], 9:
[18]}
{2: [4], 3: [6], 4: [1, 8], 5: [10], 6: [12], 7: [2, 14], 8: [16], 9: [18]}
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