  Complex systems may morph between structures with different dimensionality
and degrees of freedom. As a tool for their modelling, nonlinear embeddings are
introduced that encompass objects with different dimensionality as a continuous
parameter $\kappa \in \mathbb{R}$ is being varied, thus allowing the
unification of vectors, matrices and tensors in single mathematical structures.
This technique is applied to construct warped models in the passage from
supergravity in 10 or 11-dimensional spacetimes to 4-dimensional ones. We also
show how nonlinear embeddings can be used to connect cellular automata (CAs) to
coupled map lattices (CMLs) and to nonlinear partial differential equations,
deriving a class of nonlinear diffusion equations. Finally, by means of
nonlinear embeddings we introduce CA connections, a class of CMLs that connect
any two arbitrary CAs in the limits $\kappa \to 0$ and $\kappa \to \infty$ of
the embedding.
