Elementary Cellular Automaton Dynamics as Wavelets

Mathematical tools from signal processing can be used to study cellular automata (CA). This Demonstration shows an example of plotting CA dynamics as a wavelet. The CA dynamics consist of the sum of black cells along each row, which represents time. The wavelet is constructed by a process of scaling and translating a signal and separating different frequency components; the graphical representation of the signal highlights the oscillatory behavior (frequency over time). It is possible to observe the four classes of CA behavior as the CA's wavelet form, more complex classes such as III and IV are noisy and harder to distinguish between one another, and classes I and II are simpler.
Class I tends to involve as a set of white or black cells, dying out.
Class II tends to be periodic.
Class III is random.
Class IV comes up with local random structures.



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

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 © 2018 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+