  Here we introduce simple structures for the analysis of complex hypergraphs,
hypergraph animals. These structures are designed to describe the local node
neighbourhoods of nodes in hypergraphs. We establish their relationships to
lattice animals and network motifs, and we develop their combinatorial
properties for sparse and uncorrelated hypergraphs. We make use of the tight
link of hypergraph animals to partition numbers, which opens up a vast
mathematical framework for the analysis of hypergraph animals. We then study
their abundances in random hypergraphs. Two transferable insights result from
this analysis: (i) it establishes the importance of high-cardinality edges in
ensembles of random hypergraphs that are inspired by the classical
Erd\"os-Reny\'i random graphs; and (ii) there is a close connection between
degree and hyperedge cardinality in random hypergraphs that shapes animal
abundances and spectra profoundly. Both findings imply that hypergraph animals
can have the potential to affect information flow and processing in complex
systems. Our analysis of also suggests that we need to spend more effort on
investigating and developing suitable conditional ensembles of random
hypergraphs that can capture real-world structures and their complex dependency
structures.
