Wolfram Computation Meets Knowledge

Wolfram Summer School


Zhe Hu

Summer School

Class of 2004


Zhe Hu was born in the People’s Republic of China in 1976. He got his bachelor’s degree in Electrical Engineering in 1999 and master’s degree in Biomedical Engineering in 2001 from Tongji University, China. He is currently pursuing his Ph.D. in Biomedical Engineering at the Illinois Institute of Technology, Chicago. There he is working on a cortical visual prostheses and implants project. His research interests are both computational neuroscience and the advanced technology for neural stimulation. The application of NKS is also of great attraction to him. He likes reading and programming, especially programming in Mathematica.

Project: Searching for Texture-Sensitive Selector Using 2D Cellular Automata

Human eyes can easily pick out certain texture information from 2D images generated by 1D or 2D cellular automata (CA). The objective of this project is to find a simple computer program that performs a similar job. Consider irreversible image compression or pattern recognition in which a CA plays the part traditionally played by a statistics model or a trained neural network. The advantage granted by NKS over traditional neural networks is that we have a known search space.

Since our visual system has a cascade of processing stages, it could be possible that we recognize patterns at larger scale by applying simple rules twice or more. Accordingly, applying ECA rules two steps acts at range 2. As the number of steps increases, the longer range things get involved. So if we choose to model the system as ECA with multiple steps, it will inevitably introduce nonlinear behavior into the system, but it might reduce the parameters of the model to achieve a simple model with large capacity. That is the kind of modeling approach NKS favors.

The conclusions drawn from studying these 1D cases are that models with a short-range rule can have long-range “vision”, and that probably more nonlinear behaviors are involved when these short-range rules recognize long-range patterns.

If we choose 9-neighbor totalistic rules in 2D CA and apply the rules for multiple steps, the system has complex and rich nonlinear behavior. As in the clustering of ECA images case, the search program found 18 rules that can classify the images further than the 16 templates as shown on page 581 of A New Kind of Science. There are many other such interesting creatures living in the nonlinear land. They are worth searching for.

We don’t have a general pattern recognizer that can look for patterns itself yet, though we have found some rules like edge detector and triangle finder that can extract features from an image.

Favorite Two-Color, Radius-2 Rule

Rule chosen: 2147265820

I am interested in finding rules that generate complex behavior from a simple initial condition (a single black cell to start from). Since the rule 30 elementary cellular automaton is such a case, I try to find rules that can generate patterns that look close enough to rule 30. The result (the first of such rules I found) is rule 2147265820.