Shahid Beheshti UniversityCategories and General Algebraic Structures with Applications2345-58533120150701$omega$-Operads of coendomorphisms and fractal $omega$-operads for higher structures658810527ENCamellKachourDepartment of Mathematics, Macquarie University, Sydney, Australia.Journal Article20150824 In this article we introduce the notion of textit{Fractal $omega$-operad} emerging from a natural $omega$-operad associated to any coglobular object in the category of higher operads in Batanin's sense, which in fact is a coendomorphism $omega$-operads. We have in mind coglobular object of higher operads which algebras are kind of higher transformations. It follows that this natural $omega$-operad acts on the globular object associated to these higher transformations. To construct the natural $omega$-operad we introduce some general technology and give meaning to saying an $omega$-operad possesses the textit{fractal property}. If an $omega$-operad $B^{0}_{P}$ has this property then one can define a globular object of all higher $B^{0}_{P}$-transformations and show that the globular object has a $B^{0}_{P}$-algebra structure.http://cgasa.sbu.ac.ir/article_10527_391dbbec71f3cd9c77ef8d4d484a2ed9.pdf