How about a countably infinite string of machines similar to my original 
machines but having no input where at each print cycle each machine prints 
a one or zero at random.

The stings they produce read left to right or right to left is a number = a 
universe configuration.   Eventually some selection of output numbers will 
match the sequence of numbers for any universe.  A particular universe 
would not necessarily get its next number right away - it would usually 
wait a random number of print cycles to get to its next number while some 
other universes get their next number.

That seems to work.


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