  We explore a new way to simulate quantum field theory, without introducing a
spatial lattice. As a pilot study we apply this method to the 3d \lambda \phi^4
model. The regularisation consists of a fuzzy sphere with radius R for the two
spatial directions, plus a discrete Euclidean time. The fuzzy sphere
approximates the algebra of functions of the sphere with a matrix algebra, and
the scalar field is represented by a Hermitian N x N matrix at each time site.
We evaluate the phase diagram, where we find a disordered phase and an ordered
regime, which splits into phases of uniform and non-uniform order. We discuss
the behaviour of the model in different limits of large N and R, which lead to
a commutative or to a non-commutative \lambda \phi^4 model in flat space.
