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: <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> <-> ...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.