{1,1} Surface Deposition with {-1,1} Growth

Deposition material is deposited from the top toward the bottom. This deposit is allowed to stick only to the top of the substrate or to the top of the deposit. Cells embedded in the substrate's surface represent defects in that substrate and are not allowed to fill. The region above the substrate is assumed to be evacuated. The surface reconfigures itself with every cycle.
The computation is performed by a search-update-feedback cellular automaton (SCA). The control "animate growth" triggers the SCA; toggle the "reset" control to restart with a new surface configuration, or check this control to change the surface size; uncheck "reset" to restart.


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


Activation energy, bond strength, charging, diffusion, and thermal effects are not considered in the computation—vacant site deposition and post-deposition growth is based on neighborhood configuration rules alone.
Check the "quantify growth" control at any time to switch between the matrix plot simulation of the growth and a network quantification of this simulation. Color information is synchronized between these two views; change the color setting at any time. The quantification is exhaustive on a per cell basis.
With "quantify growth" checked, check the "directed edges" control to follow the information flow throughout the surface (use the "directed edges" control with any of the network embedding methods; linear embedding is informative with both settings of this control). Edge colors are determined by the datum of the vertex a given arrow points to; vertex formats are shown below.
Use the control "edges and vertices" or "vertices only" to get vertex information (please note that "vertices only" has precedence)—pause and mouseover a vertex of interest to locate it on the surface. Vertices have this format: {{cell row, cell column}, cell state}.
[1] B. Chopard and M. Droz, Cellular Automata Modeling of Physical Systems, Cambridge: Cambridge University Press, 2005.
[2] R.C. Jaeger, Introduction to Microelectronic Fabrication: Modular Series on Solid State Devices, Vol. V., Reading, MA: Addison–Wesley, 1993.
[3] A.B. Glaser and G.E. Subak–Sharpe, Integrated Circuit Engineering, Reading, MA: Addison-Wesley, 1979.
[4] Wikipedia, "Sputtering." (Jun 14, 2013) en.wikipedia.org/wiki/Sputtering.
[5] Wikipedia, "Negative Feedback." (Jun 14, 2013) en.wikipedia.org/wiki/Negative_feedback.
[6] Wikipedia, "Positive Feedback." (Jun 14, 2013) en.wikipedia.org/wiki/Positive_feedback.


    • 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+