9860

Idealized Belousov-Zhabotinsky Reaction

This Demonstration shows an idealized version of the Belousov-Zhabotinsky reaction implemented by means of a two-dimensional, totalistic cellular automaton.

THINGS TO TRY

SNAPSHOTS

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

DETAILS

NKS can describe self-organization of complex chemical and biological spatial structures. Sometimes some of these structures can share the same pattern. For instance, spiral waves—studied in the past by Arthur Winfree and others—are typical of many chemical reactions, as well as in slime mold colonies. This pattern is also typical of the amoeba Dictyostelium discoideum, in which spiral structures arise from the movements of amoebae in response to propagating waves of the cAMP.
In this Demonstration, the Belousov-Zhabotinsky chemical reaction pattern is implemented by means of two-dimensional totalistic cellular automaton. This Demonstration uses a range 1, 20-color totalistic cellular automaton with rule number 1350851716507335422, but a wide number of rules around this one produce similar patterns.
Observing the pattern formation, two different spatial structures can arise: concentric waves and spiral waves. The two different patterns depend on the initial conditions and represent a clear example of multiple modes of self-organization.
For further information, see:
R. Solé and B. Goodwin, Signs of Life: How Complexity Pervades Biology, New York: Basic Books, 2000.
S. Kauffman, At Home in the Universe: The Search for the Laws of Self-Organization and Complexity, Oxford: Oxford University Press, 1995.
A. Winfree, When Time Breaks Down: The Three-Dimensional Dynamics of Electrochemical Waves and Cardiac Arrhythmias, Princeton: Princeton University Press, 1987.
    • 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 © 2014 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+