String

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String model

This applet displays a cellular automaton model of string.

The model is exactly reversible - and can be run backwards by ticking the checkbox supplied.

It uses an isometric neighbourhood - known as the Square-16 partitioning neighbourhood in order to produce a reversible system. This is a larger version of the Square-4 partitioning neighbourhood.

While it is a development of the "membrane" model, it uses a much larger neighbourhood and uses a much smaller number of states per cell - and makes no attempt to model links explicitly.

Partition rules

The automaton can be thought of as consisting of three layers:

  • Simple gas - used solely as a source of biased pseudo-random numbers (and not displayed);
  • Diffusing gas - used to greate pressure between the membranes;
  • String cells - used to construct the strings themselves;
Each partition is divided into sixteen cells. Each cell contains one of two states - depicted as:

&

;

Cellular evolution progresses according to a large number of rules:

  • If a bit in the gas PRNG layer is set the contents of the partition remain unchanged...

  • ...otherwise the following transformations are applied:




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    ...in all rotated and reflected variations.

    If the state of the partition is not in the list above, it remains unchanged.

Some things to note about the rules:
  • The 12 edge cells are never modified;
  • The count of the number of cells is preserved;
  • No regions that were separated are ever connected;
  • The rules deal with string ends and junctions of 3 and 4 "threads".

Currently not all rules are typically used - since there is no way of moving to states containing strings that move through reflex (i.e. 315 degree) angles.

While - in principle - the strings are mobile, any string of a significant size has a powerful tendency to stay in one place.


Tim Tyler | tim@tt1.org | http://cell-auto.com/