HIGH-DIMENSIONAL AND VERY LARGE CELLULAR-AUTOMATA FOR IMMUNOLOGICAL SHAPE SPACE

Simulations with 10(9) cells 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.