  In this paper we investigate the computational power of a set of mobile
robots with limited visibility. At each iteration, a robot takes a snapshot of
its surroundings, uses the snapshot to compute a destination point, and it
moves toward its destination. Each robot is punctiform and memoryless, it
operates in $\mathbb{R}^m$, it has a local reference system independent of the
other robots' ones, and is activated asynchronously by an adversarial
scheduler. Moreover, robots are non-rigid, in that they may be stopped by the
scheduler at each move before reaching their destination (but are guaranteed to
travel at least a fixed unknown distance before being stopped).
  We show that despite these strong limitations, it is possible to arrange
$3m+3k$ of these weak entities in $\mathbb{R}^m$ to simulate the behavior of a
stronger robot that is rigid (i.e., it always reaches its destination) and is
endowed with $k$ registers of persistent memory, each of which can store a real
number. We call this arrangement a TuringMobile. In its simplest form, a
TuringMobile consisting of only three robots can travel in the plane and store
and update a single real number. We also prove that this task is impossible
with fewer than three robots.
  Among the applications of the TuringMobile, we focused on Near-Gathering (all
robots have to gather in a small-enough disk) and Pattern Formation (of which
Gathering is a special case) with limited visibility. Interestingly, our
investigation implies that both problems are solvable in Euclidean spaces of
any dimension, even if the visibility graph of the robots is initially
disconnected, provided that a small amount of these robots are arranged to form
a TuringMobile. In the special case of the plane, a basic TuringMobile of only
three robots is sufficient.
