ω-Operads of coendomorphisms and fractal ω-operads for higher structures

In this article we introduce the notion of \textit{Fractal ω-operad} emerging from a natural ω-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism ω-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural ω-operad acts on the globular object associated to these higher transformations. To construct the natural ω-operad we introduce some general technology and give meaning to saying an ω-operad possesses the \textit{fractal property}. If an ω-operad B0P has this property then one can define a globular object of all higher B0P-transformations and show that the globular object has a B0P -algebra structure.