  This survey may be seen as an introduction to the use of toric and tropical
geometry in the analysis of plane curve singularities, which are germs $(C,o)$
of complex analytic curves contained in a smooth complex analytic surface $S$.
The embedded topological type of such a pair $(S, C)$ is usually defined to be
that of the oriented link obtained by intersecting $C$ with a sufficiently
small oriented Euclidean sphere centered at the point $o$, defined once a
system of local coordinates $(x,y)$ was chosen on the germ $(S,o)$. If one
works more generally over an arbitrary algebraically closed field of
characteristic zero, one speaks instead of the combinatorial type of $(S, C)$.
One may define it by looking either at the Newton-Puiseux series associated to
$C$ relative to a generic local coordinate system $(x,y)$, or at the set of
infinitely near points which have to be blown up in order to get the minimal
embedded resolution of the germ $(C,o)$ or, thirdly, at the preimage of this
germ by the resolution. Each point of view leads to a different encoding of the
combinatorial type by a decorated tree: an Eggers-Wall tree, an Enriques
diagram, or a weighted dual graph. The three trees contain the same
information, which in the complex setting is equivalent to the knowledge of the
embedded topological type. There are known algorithms for transforming one tree
into another. In this paper we explain how a special type of two-dimensional
simplicial complex called a lotus allows to think geometrically about the
relations between the three types of trees. Namely, all of them embed in a
natural lotus, their numerical decorations appearing as invariants of it. This
lotus is constructed from the finite set of Newton polygons created during any
process of resolution of $(C,o)$ by successive toric modifications.
