  The goal of this article is to exhibit two new families of finitely generated
simple groups of homeomorphisms of $\mathbf{R}$. These families are strikingly
different from existing families owing to the nature of their actions on
$\mathbf{R}$, and exhibit surprising algebraic and dynamical features. In
particular, one construction provides the first examples of finitely generated
simple groups of homeomorphisms of the real line which also admit a minimal
action by homeomorphisms on the circle. This provides new examples of finitely
generated simple groups with infinite commutator width, and the first such left
orderable examples. Another construction provides the first examples of
finitely generated simple left orderable groups that admit minimal actions by
homeomorphisms on the torus.
