Resonators couple to each other when put in contact, leading to collective resonant modes. An interesting problem is to understand and exploit these collective modes when the resonators form different patterns in space. In this talk I will first present a kaleidoscope of numerical examples where patterned resonators display spectral properties akin to 2- and higher-dimensional Integer Quantum Hall Effect. In the second part, I will demonstrate how K-theory can be used to understand and predict the bulk and the edge spectrum of such systems. In particular, a simple K-theoretic version of the bulk-boundary principle will be presented which enables one to see when topological edge spectrum is to be expected. This last part will be supported again with a kaleidoscope of numerical examples.