gravity index
  the good source
click to launch  fullscreen in new window

Levitated Houyhnhnm

Here we have evolved an intricately connected network of nodes using a single substitution rule. The network will gradually zoom in as it becomes more and more complex.

Use the mouse to explore. Click individual nodes to accelerate evolution.

Stephen Wolfram suggests many interesting methods of evolving a network using substitution systems in chapter 9 of his book A New Kind of Science. The simplest of these, a three node sub-network substitution (page 509), has been implemented in Flash MX.

figure a. the node substitution rule

The network is evolved by replacing random nodes with a subnetwork of three nodes. One prerequisite of this substitution rule is that the node being replaced must have precisely three connections.

Starting with an initial network of precisely four nodes, each connected to all three others, repeated substitutions will create a network exhibiting intricate localized structures. The nodes are intentionally left still after substitutions to add a sense of legacy. The size of the nodes decrease proportional to the length of their connections.

figure b. an evolved network using 210 substitutions

  The network will occasionally drift into vast areas of nothing. If this should happen, reload the page and the network will be reset.  
  jtarbell, march 2003  

open source Flash
commercial free open source since 2012 human generator download Flash source