  This paper gives two methods for constructing associative 3-folds in R^7,
based around the fundamental idea of evolution equations, and uses these
methods to construct examples of these geometric objects. The paper is a
generalisation of the work by Joyce in math.DG/0008021, math.DG/0008155,
math.DG/0010036 and math.DG/0012060 on special Lagrangian 3-folds in C^3. The
two methods described involve the use of an affine evolution equation with
affine evolution data and the area of ruled submanifolds.
  We first give a derivation of an evolution equation for associative 3-folds
from which we derive an affine evolution equation using affine evolution data.
We then use this on an example of such data to construct a 14-dimensional
family of associative 3-folds. One of the main result of the paper is then an
explicit solution of the system of differential equations generated in a
particular case to give a 12-dimensional family of associative 3-folds. We also
find that there is a straightforward condition that ensures that the
associative 3-folds constructed are closed and diffeomorphic to S^1xR^2, rather
than R^3.
  In the final section we define ruled associative 3-folds and derive an
evolution equation for them. This then allows us to characterise a family of
ruled associative 3-folds using two real analytic maps that must satisfy two
partial differential equations. We finish by giving a means of constructing
ruled associative 3-folds M from r-oriented two-sided associative cones M_0
such that M is asymptotically conical to M_0 with order O(r^{-1}).
