Mobile membranes

## Mobile membrane model

This applet displays a cellular automaton model of mobile membranes.

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

It uses a complex neighbourhood - which has no name. The neighbourhood is based on the idea described here."

## 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;
• Links - used to construct the membranes themselves.
Aside from the two gasses in the model, each cell has 16 states - which are used to store the state of the atoms and links.

These arerepresented as:

A membrane is represented by a chain of links - e.g.:

Think of the red links extending to the centre of the adjacent cell for this diagram to make sense.

Cellular evolution progresses according to a few simple rules:

• If a bit in the gas PRNG layer is set then the membrane remains locally unchanged...

• ...otherwise a transformation is applied:

Information is read from the marked region:

...is transformed, and then written back to the region:

Areas that are not marked as being "written back to" are left unchanged.

Note that there are two "main" cells involved (in the top diagram) - and all the links link to one or other of them.

The rule is essentially a fairly simple one. However I'll describe it rather than attemping to exactly specify it.

If a cell is considered to be "active" if any links point at its centre, and "empty" otherwise. If either of the two "main" cells is active - and the other is empty - it moves over, updating any links as it does so (so they remain linked to the same points).

The criterion used to determine whether a cell can move in one direction is to check whether there are any links attached to it which have a component in the opposite direction. If not - that cell can move (any such links would be stretched beyond breaking point if the cell moved away from them otherwise.

This transformation is applied to the grid using the following pattern:

The diagram shows the domain above repeated in a chequer-board pattern - repeated 16 times. Domains overlap with one another at their corners, and - since I'm not using enough colours - the pattern can be a bit difficult to work out.

The rule is applied in sequence, using one of four spatial offsets: (0,0), (0,1), (1,0) and (1,1).

This is the "horizontal" rule. There's also a "vertical" rule:

Information is read from the marked region:

...is transformed, and then written back to the region:

Areas that are not marked as being "written back to" are left unchanged.

The transformation above is applied to the grid using the following pattern:

Note that - in the applet - a cell is displayed as containing membrane if there are any links in that cell. Unfortunately, this produces some visible gaps - as a look at the diagram of the "example" membrane near the top of this document illustrates.

A better-quality display routine would mark cells if they had any links going into them.

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