11284

One-Dimensional Cellular Automata with Memory

This Demonstration shows an implementation of memory in one-dimensional cellular automata. We use two kinds of memory mechanisms (average -type memory and majority memory) to first determine the cell trait states, based on their past states, and then apply the formally unchanged updating rule. Average memory acts by means of a weighting mechanism based on a memory factor . Majority memory acts by selecting the most frequent of the last states. Both types of memory are shown simultaneously for comparison. Initial states can be chosen between one single seed or a random set. Perturbation analysis may also be visualized.

SNAPSHOTS

  • [Snapshot]
  • [Snapshot]
  • [Snapshot]

DETAILS

Cellular automata (CAs) are discrete systems usually defined to be updated using rules that read only the previous state of each cell and its neighbors: . Here we change this approach by recovering the cell state history but keeping the updating rules the same. Memory is defined to be, for each cell, the summary of its previous states, acting according to a simple mechanism (average or majority) in order to determine the whole instance of the update rule: . It is important to note that remains unchanged. On the contrary, the trait states are those that change, summarizing the history of the cell states.
In the case of the average memory, we use a weighting factor of , albeit in two-state CAs, -memory has no effect if . For the case of the majority memory, we use the previous states in order to determine the most frequent of them. New and interesting phenomena can be produced with this kind of memory implementation. In particular, complex behavior may emerge from previously known chaotic rules through this implementation.
References:
[1] R. Alonso-Sanz, Discrete Systems with Memory, Singapore: World Scientific, 2011.
[2] R. Alonso-Sanz, "A Structurally Dynamic Cellular Automaton with Memory in the Triangular Tessellation," Complex Systems, 17(1), 2007 pp. 1–15. www.complex-systems.com/abstracts/v17_i01_a01.html.
[3] R. Alonso-Sanz, M. Martin, "One-Dimensional Cellular Automata with Memory in Cells of the Most Frequent Recent Value," Complex Systems, 15(3), 2005 pp. 203–236. www.complex-systems.com/abstracts/v15_i03_a02.html.
[4] R. Alonso-Sanz, M. Martin, "Elementary Cellular Automata with Memory," Complex Systems, 14(2), 2003 pp. 99–126. www.complex-systems.com/abstracts/v14_i02_a01.html.
[5] R. Alonso-Sanz, L. Bull, "Elementary Cellular Automata with Minimal Memory and Random Number Generation," Complex Systems, 18(2), 2009 pp. 195–213. www.complex-systems.com/abstracts/v18_i02_a02.html.
[6] G. J. Martinez, A. Adamatzky, R. Alonso-Sanz, J. C. Seck-Touh-Mora, "Complex Dynamics Emerging in Rule 30 with Majority Memory," Complex Systems, 18(3) 2009 pp. 345–365. www.complex-systems.com/abstracts/v18_i03_a05.html.
[7] Ramon Alonso-Sanz. (Jun 8, 2015) uncomp.uwe.ac.uk/alonso-sanz.
    • Share:

Embed Interactive Demonstration New!

Just copy and paste this snippet of JavaScript code into your website or blog to put the live Demonstration on your site. More details »

Files require Wolfram CDF Player or Mathematica.









 
RELATED RESOURCES
Mathematica »
The #1 tool for creating Demonstrations
and anything technical.
Wolfram|Alpha »
Explore anything with the first
computational knowledge engine.
MathWorld »
The web's most extensive
mathematics resource.
Course Assistant Apps »
An app for every course—
right in the palm of your hand.
Wolfram Blog »
Read our views on math,
science, and technology.
Computable Document Format »
The format that makes Demonstrations
(and any information) easy to share and
interact with.
STEM Initiative »
Programs & resources for
educators, schools & students.
Computerbasedmath.org »
Join the initiative for modernizing
math education.
Step-by-Step Solutions »
Walk through homework problems one step at a time, with hints to help along the way.
Wolfram Problem Generator »
Unlimited random practice problems and answers with built-in step-by-step solutions. Practice online or make a printable study sheet.
Wolfram Language »
Knowledge-based programming for everyone.
Powered by Wolfram Mathematica © 2017 Wolfram Demonstrations Project & Contributors  |  Terms of Use  |  Privacy Policy  |  RSS Give us your feedback
Note: To run this Demonstration you need Mathematica 7+ or the free Mathematica Player 7EX
Download or upgrade to Mathematica Player 7EX
I already have Mathematica Player or Mathematica 7+