A combinatorial graph contains much information, its Laplace spectrum, its Cheeger constant,....  Other information can determine ways by which it can evolve, say involving the parity of degrees and distance between its vertices; see my article in Mind and Matter 2013.  Okay, so I made up these rules:  it's not going to evolve under its own steam.  But wait a minute.  Our brains do a pretty good job of functioning autonomously.  Most of the time we are reacting to external stimuli, but when we sleep neurons are firing, electrical and chemical signals are transmitted, a world is being created inside our heads. 

The human brain has been described as the most complex object in the known universe, so to get a hold on how it functions, let's start with something smaller: a combinatorial graph, or better still a quantum network and try to undestand how form and change (a causal sequence) can emerge from such structure.  If we draw line segments on a piece of paper in the right way, we see a cube, in fact two possible cubes and we can flip from one to the other.   The visualization of a cube is known to psychologists as the gestalt effect, whereby we see whole forms rather than just a collection of line segements.  In my article Journal of Geometry and Physics 2013, I formalize this effect with the notion of geometric state.   A graph has a different spectrum to its Laplace spectrum, which I call its geometric spectrum, which yields local realizations of the graph as an invariant framework  in Euclidean space  (see Linear Algebra and its Applications 2014).  Projections of these realization to the complex plane satisfy a quadratic difference equation, independently of any similarity transformation (the spectrum is a parameter of this equation).  This removes the dependence on the ambient space and reveals geometry, or form, as an emergent concept. 

Introduce choice into this model and one has an example of quantum interaction, an emerging discipline which applies the methods of quantum theory to other areas of informatics Quantum Interaction .  In the geometric model discussed above, quantum interaction occurs in the two possible perceptions of the cube, in the quadratic difference equation (whose linearization is like the Schroedinger equation) satisfied by its projection to the complex plane, and the fact that only these realizations solve this equation for the given value of the geometric spectrum.

Other aspects of this project concern the reconstruction of 3D-images and the efficient encoding of geometric information.