As you may recall, a Turing-machine is an all-purpose computer. A Turing-machine has a memory that consists of a track or line of data. On the track, a read-/write-head is moving. The read-write head itself is a state engine, which is affected by the input from the track, and which decides what to write on the track, and where to read the next input, by "moving" the head back or forth.
In 5050, the part of the track left of the head is represented not by a line or stack of information, but by a binary tree. The part right of the head is represented by a binary tree, too. The head itself sort of sits between the two trees, but will often change its state according to information from the right side of the left side. In 5050, the state of the head itself is again represented as a tree of commands, although for simple programs, a linear representation can be sufficient.
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