Autocatalytic Systems

autocatalytic-automata

The above is a self-replicating dynamic structure from a class of systems called cellular automata (click here to run the simulation).  Below is a self-replicating dynamic structure from a class of systems called “life”:

The following video explores a new type of self-replicating dynamic structure that will emerge in some form or another in the coming years:

What is common to all of these examples is a property called “autocatalysis”.* More accurately, these examples are instances of cross-catalytic systems:

In reality there are only ever cross-catalytic systems (never autocatalytic) since all real systems require input from the outside (energy, information, material resources) and produce output (waste, information, resources that feed into other systems).  For physicists, this is similar to observing that there are no such things as thermodynamically closed systems in nature, and for the mathematically-inclined we can observe that we never find perfect circles in the actual universe (just in our abstract models).

One interesting idea that was postulated in the RepRap video is that:  “anything that copies itself inevitably comes under Darwin’s law of natural selection.”  Strictly speaking this is not true.  Darwinian natural selection requires two additional properties besides autocatalysis: (1) heritable variation, and (2) differential replication rates over the aforementioned variation.  But we can cut Dr. Bowyer some slack because implicit in his slide on the subject he covers both additional prerequisites for RepRap to “go Darwinian”:

reprap-evolution

Which brings me back full circle (self-referentially autocatalytic?) to the first example above of the cellular automaton (CA).  There are an infinite number of types of CAs that are distinguishable based on their rules for how one generation of cells transforms into the next.  The name of this particular CA is “Life.”**

In Life it has been proven mathematically that self-replicators (i.e. autocatalytic systems) exist, but nobody has yet found one.  [As an aside, this doesn’t contradict my previous point about all autocatalytic systems really being cross-catalytic since the system that Life runs on (i.e. computer + software) really should be considered part of the system being replicated, strictly speaking.]  Given the complexity of the search space, it seems likely that the best way to find such an autocatalytic Life pattern would be via evolutionary itself.

If anyone is looking for a doctoral project, finding a self-replicator in the Game of Life would be a worthy goal.



* When people who work in complexity speak about “self-organization”, autocatalysis is one important form, but not the only form.  Cooperation represents a large class of self-organizing behavior as well.  Both autocatalysis and cooperation lead to emergence of new levels of complexity.

** the full name is Conway’s Game of Life, named for it’s discoverer.