This research concerns fault-tolerant cellular automata (FTCA). Such automata require generally elaborate constructions. The notions introduced in previous years enable us to make the newer costructions much more transparent. All known FTCA rely heavily on the fact that the cells of the whole array update simultaneously. FTCA with asynchronous updation are being constructed. All known FTCA in dimensions lower than 3 must be prepared in an elaborate, hierarchical initial configuration. Techniques for building a FTCA without this requirement are being investigated. In this homogenous medium, arbitrarily complex noise-resistant structures arise spontaneously. The complexity is understood in the sense of carrying out complex computational tasks. The mathematical possibility of such a medium is significant for physics and biology as well as computer science. The computational and informational costs of all constructions are generally found to be near the theoretical minimum.
