  Global amoebas are a wide and rich family of graphs that emerged from the
study of certain Ramsey-Tur\'an problems in $2$-colorings of the edges of the
complete graph $K_n$ that deal with the appearance of unavoidable patterns once
a certain amount of edges in each color is guaranteed. Indeed, it turns out
that, as soon as such coloring constraints are satisfied and if $n$ is
sufficiently large, then every global amoeba can be found embedded in $K_n$
such that it has half its edges in each color. Even more surprising, every
bipartite global amoeba $G$ is unavoidable in every tonal-variation, meaning
that, for any pair of integers $r, b$ such that $r + b $ is the number of edges
of $G$, there is a subgraph of $K_n$ isomorphic to $G$ with $r$ edges in the
first color and $b$ edges in the second. The feature that makes global amoebas
work are one-by-one edge replacements that leave the structure of the graph
invariant. By means of a group theoretical approach, the dynamics of this
feature can be modeled. As a counterpart to the global amoebas that "live"
inside a possibly large complete graph $K_n$, we also consider local amoebas
which are spanning subgraphs of $K_n$ with the same feature.
  In an effort to highlight their richness and versatility, we present here
three different recursive constructions of amoebas, two of them yielding
interesting families per se and one of them offering a wide range of
possibilities.
