  We present a new method, called the pixel array method, for approximating all
solutions in a bounding box for an arbitrary nonlinear system of relations. In
contrast with other solvers, our approach requires that the user must specify
which variables are to be exposed, and which are to be left latent. The entire
solution set is then obtained---in terms of these exposed variables---by
performing a series of array multiplications on the $n_i$-dimensional plots of
the individual relations $R_i$. This procedure introduces no false negatives
and is much faster than Newton-based solvers. The key is the unexposed
variables, which Newton methods can make no use of. In fact, we found that with
even a single unexposed variable our method was more than 10x faster than
Julia's NLsolve. Due to its relative simplicity, the pixel array method is also
applicable to a broader class of systems than Newton-based solvers are. The
purpose of this article is to give an account of this new method.
