  In a probabilistic cellular automaton in which all local transitions have
positive probability, the problem of keeping a bit of information indefinitely
is nontrivial, even in an infinite automaton. Still, there is a solution in 2
dimensions, and this solution can be used to construct a simple 3-dimensional
discrete-time universal fault-tolerant cellular automaton. This technique does
not help much to solve the following problems: remembering a bit of information
in 1 dimension; computing in dimensions lower than 3; computing in any
dimension with non-synchronized transitions.
  Our more complex technique organizes the cells in blocks that perform a
reliable simulation of a second (generalized) cellular automaton. The cells of
the latter automaton are also organized in blocks, simulating even more
reliably a third automaton, etc. Since all this (a possibly infinite hierarchy)
is organized in ``software'', it must be under repair all the time from damage
caused by errors. A large part of the problem is essentially self-stabilization
recovering from a mess of arbitrary size and content. The present paper
constructs an asynchronous one-dimensional fault-tolerant cellular automaton,
with the further feature of ``self-organization''. The latter means that the
initial configuration does not have to encode an infinite hierarchy -- this
will be built up over time.
  This is a corrected and strengthened version of the journal paper of 2001.
