  The research in topological materials and meta-materials reached maturity and
is now gradually entering the phase of practical applications and devices.
However, scaling down the experimental demonstrations definitely presents a
challenge. In this work, we study coupled identical resonators whose collective
dynamics is fully determined by the pattern in which the resonators are
arranged. We call a pattern topological if boundary resonant modes fully fill
all existing spectral gaps whenever the pattern is halved. This is a
characteristic of the pattern and is entirely independent of the structure of
the resonators and the details of the couplings. Existence of such patterns is
proven using $K$-theory and exemplified using a novel experimental platform
based on magnetically coupled spinners. Topological meta-materials built on
these principles can be easily engineered at any scale, providing a practical
platform for applications and devices.
