In this project, we investigated the behaviour of 1 dimensional totalistic Cellular Automata (CA) from a nonlinear dynamics perspective. Our tool of choice for investigating Cellular Automata is Mathematica (version 6.0).

2. An Example

Lets compare the output of the following two commands in Mathematica:

ArrayPlot[CellularAutomaton[110, {{1}, 0}, 100]]

ArrayPlot[CellularAutomaton[193, {{1}, 0}, 100]]

The commands above plot the output from CellularAutomaton on Rule 110 and Rule 193 for 100 runs on the initial condition {1,0,0,0,...}. The output is shown below:

Rule 110: Rule 193:

Notice how closely related the two evolutions are. You can start understanding such similarities from the Introductory Reading section below.

3. Introductory Reading

The materials below should help you get upto speed on Cellular Automata.

- A New Kind of Science. Wolfram, Stephen.
- A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science. Part I: Threshold of Complexity.
**5 MB**. Chua et. al. International Journal of Bifurcation and Chaos (IJBC), Vol. 12, No. 12 (2002). pp. 2655 - 2766. - A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science. Part II: Universal Neuron.
**2.6 MB**. Chua et. al. International Journal of Bifurcation and Chaos (IJBC), Vol. 13, No. 9 (2003). pp. 2377-2491. - A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science. Part III: Predicting the Unpredictable.
**9 MB**. Chua et. al. International Journal of Bifurcation and Chaos (IJBC), Vol. 14, No. 11 (2004). pp. 3689 - 3820. - A Nonlinear Dynamics Perspective of Wolfram's New Kind of Science. Part IV: From Bernoulli Shift to 1/f Spectrum.
**6 MB**. Chua et. al. International Journal of Bifurcation and Chaos (IJBC), Vol. 15, No. 4 (2005). pp. 1045-1183.

4. Work Accomplished and Awards

Here (updated: 05/27/08) are functions that we wrote in Mathematica for investigating the evolution of Cellular Automata.

We investigated factorization properties of Cellular Automata. Here is the technical report related to our work.

Bharathwaj Muthuswamy (Prof. Chua's last graduate student) who worked on this project participated in the New Kind of Science Summer School organized by Stephen Wolfram in Pisa, Italy from June 23rd to July 11th 2009.

5. Publications

- Optimal Cellular Neural Network Templates for Linearly Separable 1D Cellular Automata. Muthuswamy, Bharathwaj and Chang, JoJo. International Journal of Bifurcation and Chaos (IJBC). Vol. 17, No. 3 (2007). pp. 749 - 791.

Page last updated: September 2009