graphs

Random Graphs in Time and 2D Space

29 Jun 2009

Posted by doug

summary:

Random graphs in a plane can be relevant for where to place cell phone towers, so this topic is studied commercially.

description:

There are 6000 nodes used in this animation. How many survived by being close enough to another node is not known.

command:

q_graph -dir networks -out random_3d_6000_y -box 1.2 -command generate_random_network -nodes 6000 -fix_y -1

math

equation:

Link nodes if dt < 0.05 and |dx|+|dz| < 0.15, y = -1

numbers:

random_3d_6000_y.povray.100.1000.numbers

Random Graphs in Time and 3D Space

29 Jun 2009

Posted by doug

summary:

Some 6000 nodes were generated, and if close enough in both time and space, were linked together. There is no pattern here, and none was expected.

description:

A random graph in spacetime looks both random and transient. It might be interesting to know how many of these short paths have branches. For this initial sketch, I did not provide a means of tracking the more complicated graphs.

command:

q_graph -dir networks -out random_3d_6000 -box 1.2 -command "generate_random_network -nodes 6000"

math

equation:

Link nodes if dt < 0.05 and |dx|+|dy|+|dz| < 0.15

numbers:

random_3d_6000.povray.100.1000.numbers

29 Jun 2009

Posted by doug

Graph theory details how things are connected. There are nodes that are connected by edges. The edges can either be directional or undirectional. Here is the graph for real number multiplication:

Tags:

graphs

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