Revisions to "The" random tree

Indentation fix in Sage code.

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edited Dec 26, 2013 at 13:16

Samuele Giraudo

437
1
4
15

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/newuploads/ta8ni.png

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/newuploads/3yl9z.png

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/newuploads/qqcm4.png

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
    return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/newuploads/ta8ni.png

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/newuploads/3yl9z.png

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/newuploads/qqcm4.png

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/newuploads/ta8ni.png

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/newuploads/3yl9z.png

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/newuploads/qqcm4.png

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
    return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

corrected image links - as discussed on meta: http://meta.mathoverflow.net/questions/1012/inline-images-not-displaying-correctly

Source Link

edit approved Oct 12, 2013 at 17:00

Martin Sleziak

4.7k
4
35
40

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/ta8ni The random tree over 32 nodes. http://www.freeimagehosting.net/newuploads/ta8ni.png

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/3yl9z The random tree over 96 nodes. http://www.freeimagehosting.net/newuploads/3yl9z.png

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/qqcm4 The random tree over 512 nodes. http://www.freeimagehosting.net/newuploads/qqcm4.png

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/ta8ni

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/3yl9z

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/qqcm4

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/newuploads/ta8ni.png

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/newuploads/3yl9z.png

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/newuploads/qqcm4.png

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

added 1 characters in body; added 12 characters in body; added 4 characters in body

Source Link

edited Mar 5, 2013 at 22:00

Samuele Giraudo

437
1
4
15

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/ta8ni

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/3yl9z

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/qqcm4

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 124, vertex_labels = False, graph_border = True, iterations = 4096)

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/ta8ni

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/3yl9z

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/qqcm4

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
tree = Graph()
tree.add_vertex(1)
for i in xrange(2, n + 1) :
    tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 1, vertex_labels = False, graph_border = True, iterations = 4096)

Here are some pictures of the random tree reduced over a finite number of nodes.

Over $32$ nodes: The random tree over 32 nodes. http://www.freeimagehosting.net/ta8ni

Over $96$ nodes: The random tree over 96 nodes. http://www.freeimagehosting.net/3yl9z

Over $512$ nodes: The random tree over 512 nodes. http://www.freeimagehosting.net/qqcm4

I employ the following ${\tt Sage}$ code to generate these:

def random_tree(n) :
    tree = Graph()
    tree.add_vertex(1)
    for i in xrange(2, n + 1) :
        tree.add_edge(i, randint(1, i - 1))
return tree

and the following code to draw these:

tree = random_tree(32)
tree.plot(vertex_size = 24, vertex_labels = False, graph_border = True, iterations = 4096)

Source Link

created Mar 5, 2013 at 21:53

Samuele Giraudo

437
1
4
15

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