Wolfram Computation Meets Knowledge

Wolfram Summer School


Nima Dehghani

Summer School

Class of 2014


My research lies at the intersection of physics, computation, and neuroscience, with aims toward understanding the computational foundations of neural information processing. The trajectory of my past, present research, and future goals have many parallels with the grand challenges where computation meets natural science. My research can be divided into several inseparable frontiers: a) to decipher computational foundations characterized by dynamic patterns of neuro-signals obtained from miniaturized high-throughput micro-devices and large-scale recordings, b) to understand the complexity and biophysical nature of the measured signal at multiple spatiotemporal scales, c) to explore the emergent dynamics in information processing networks, and d) to predict the behavior of high-throughput signals with higher accuracy and further enhance their usability for translational purposes.

Project: Interacting Cellular Automaton


Certain physical systems are composed of coupled oscillators. The connection between the oscillators forms the link through which the energy can be transferred between them. The motion of such oscillators could range from orderly (periodic) to complex (chaotic). Some systems harbor different levels of coupling across their constituent scales. For example, in solids, inter-atomic coupling force is many orders of magnitude stronger than the forces that link the atoms to equilibrium positions. Therefore, in systems of many scales of length, it is essential to map the landscape within which the interleaved layers of coupling of different degrees dicatate the evolutionary fate of the system.

Specific Aims

In this project, I will specifically look at the interaction of two CA systems that are linked with each other. Specific aims are:

  1. Map the effects of intrinsic (within CAs) connectivity on the dynamics of the interacting CAs.
  2. Map the effects of extrinsic (between CAs) connectivity on the dynamics of the interacting CAs.
  3. Map the effects of intrinsic rules vs. extrinsic rules on the dynamics of the interacting CAs.


I will start with simple 1D systems to map the classes of interaction between two CAs. In each CA, I will define a local neighborhood rule which we call “intrinsic connectivity”. The “extrinsic connectivity” will define how the elements of the two CAs are connected with each other. It is through these extrinsic connections that the dynamics of a given system influences the other CA and vice versa. In the first step, I will use the same “intrinsic rules” of totalistic type to define how cells of a given CA update their values. Then by varying the degrees of extrinsic connectivity, I will catalog the dynamics of the two interacting CAs.

In the next stage, I will use different sorts of intrinsic rules for each of the two interacting CAs. Then I will follow the same steps to follow the evolution of the two CAs. For better visualization, I will adapt a tricolor system to follow the trends of the cells that are solely influenced by their parent CA as well as cells that are influenced by the interacting CA dynamics. I will use parallel visualization of the two systems to better map their dynamics through their course of interaction.

In the last phase, I will search for cases where the interaction may lead to explosive activation of cells in a given CA. Then I will search for the rules that could be applied to remove links (by modifying the extrinsic connectivity) that could stop such explosive activity of cells.

Future plans

These early investigations will pave the way for future explorations of coupled systems of many length scales that I will follow in the future. After classifying the possible types of interaction between two simple 1D systems, I aim to extend the studies to many coupled CAs. In the phase to follow I will extend the studies to higher dimensions.

Favorite Outer Totalistic r=1, k=2 2D Cellular Automaton

Rule 248258