  One of the questions addressed here is How can a twisted thread correct
itself?. We consider a theoretical model where the studied mathematical object
represents a 2D twisted discrete thread linking two points. This thread is made
of a chain of agents which are lost, i.e. they have no knowledge of the global
setting and no sense of direction. Thus, the modifications made by the agents
are local and all the decisions use only minimal information about the local
neighborhood. We introduce a random process such that the thread reorganizes
itself efficiently to become a discrete line between these two points. The
second question addressed here is to reorder a word by local flips in order to
scatter the letters to avoid long successions of the same letter. These two
questions are equivalent. The work presented here is at the crossroad of many
different domains such as modeling cooling process in crystallography [2, 3,
8], stochastic cellular automata [6, 7], organizing a line of robots in
distributed algorithms (the robot chain problem [5, 11]), and Christoffel words
in language theory [1].
