Monday, November 22, 2010

Recursive weighted skeleton

Given the weighted straight skeleton, and two features
  • The ability to change the speed of an edge at a certain time (height/offset depending on your model) (lets call this an edge direction event)
  • The ability to add edges on a particular edge at a certain time (lets call this a plan edit)
We can devise a language that allows the plan edits after a sequence of edge direction events. The question is - can this language be recursive? Turns out the answer is yes:

Here's another more discrete variant.

This is interesting because of it's similarity to two different types of automata - fractals (such as the Koch snowflake) and cellular automata (such as the game of life). Because the speed of edges can be forward or backward we can create edge direction events to model growth and decay - this is somewhat like the game of life. And because our language allows recursion we can model fractal shapes...

I get the feeling that system has the persistence and transmission of information to create high (Wolfram) classes of behaviour according to Wolfram. Will need a better implementation to go hunting for them...

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