Wolfram Computation Meets Knowledge

Wolfram Summer School


Rama Malladi

Summer School

Class of 2003


Rama’s objective is to gain practical experience in the field of electrical engineering with a major emphasis on research and software development in DSP/Image Processing. In particular his research interests include the implementation of signal processing algorithms in software and hardware, applications of wavelets and multi-resolution analysis in image processing, mathematical analysis and numerical computation. In June 2003 Rama became a Master of Science in Electrical Engineering, having researched a paper on “Applications of ICA in Synthetic Aperture Radar (SAR) image denoising” at University of Massachusetts Dartmouth. He received a Bachelor of Engineering in Electronics and Communications from Osmania University, India.

Project: Investigating the Reducibility of Cellular Automaton Outputs

Given the output (last line) of any Cellular Automaton (2-color CA set of 256 rules), to investigate and find a unique inverse/attractor CA system for that output.

The reason for studying inverse systems for the Cellular Automaton (CA) outputs is to address the issue of compression and computational irreducibility of the CA outputs. These issues were dealt in the Chapters 10 and 12 of NKS respectively. In Chapter 10 the notion of computational irreducibility of a CA output was studied by applying various compression schemes on the output and checking if there was any compression achieved. If compression of any CA output was possible, then the corresponding output was computationally reducible. In this project, I would like to investigate the issue of compression by studying the computational reducibility of the output. i.e., To check for computational irreducibility of any given output, which would then indicate if that output is compressible. Such a characterization would prove that any kind of compression scheme would have similar performance.

Favorite Three-Color Cellular Automaton

Rule Chosen: 822720519750

Reason: Another interesting observation that I made about the rule 822720519750 with offset + 6, -3 is that they show multi-scale, self-similar behavior with a mixture of regularity and irregularity. Also, these CAs grow only onto one side and progressively move towards the right in the evolution. Such a behavior I think belongs to Class – 4.