IDEAS home Printed from https://ideas.repec.org/a/wsi/ijmpcx/v04y1993i02ns0129183193000434.html
   My bibliography  Save this article

High-Dimensional And Very Large Cellular Automata For Immunological Shape Space

Author

Listed:
  • Dietrich Stauffer

    (Institute for Theoretical Physics, Cologne University, D-W-5000 Köln 41, Germany)

  • Muhammad Sahimi

    (HLRZ, KFA, D-W-5170 Jülich 1, Germany, and Department of Chemical Engineering, University of Southern California, Los Angeles, CA 90089-1211, USA)

Abstract

Simulations with109cells are made on an iPSC Hypercube with 32 parallel i860 processors, updating more than a million sites per second and per processor. This size reaches into the size range of natural immune systems. Smaller sizes are simulated in higher dimensions up to ten. These cellular automata due to de Boer. van der Laan, and Hogeweg model the idiotypic shape space and differ from usual Ising models through interactions with the mirror sites of the lattice. For majority rules (voter rules) we find Ising-like behavior with a spontaneous magnetization vanishing at some critical temperature which approaches its mean field value for high dimensions. The previously observed self-organization in the form of domain formation is thus explained as spinodal decomposition.

Suggested Citation

  • Dietrich Stauffer & Muhammad Sahimi, 1993. "High-Dimensional And Very Large Cellular Automata For Immunological Shape Space," International Journal of Modern Physics C (IJMPC), World Scientific Publishing Co. Pte. Ltd., vol. 4(02), pages 401-408.
    • Handle: RePEc:wsi:ijmpcx:v:04:y:1993:i:02:n:s0129183193000434
    DOI: 10.1142/S0129183193000434
    as

    Download full text from publisher

    File URL: http://www.worldscientific.com/doi/abs/10.1142/S0129183193000434
    Download Restriction: Access to full text is restricted to subscribers
    File URL: https://libkey.io/10.1142/S0129183193000434?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    As the access to this document is restricted, you may want to search for a different version of it.

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:wsi:ijmpcx:v:04:y:1993:i:02:n:s0129183193000434. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    We have no bibliographic references for this item. You can help adding them by using this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Tai Tone Lim (email available below). General contact details of provider: http://www.worldscinet.com/ijmpc/ijmpc.shtml .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.