Kink bands are not a musical genre, but rather are structural features in rocks. I think the things in these photos are kink bands, which are essentially tiny little angular dislocations with wavelengths on the order of a millimeter or just a bit more. Classic kink bands tend to be a little more angular than these in cross section, and they can be much larger, and mine might actually be little folds. It depends on the detailed structural evolution at a microscopic (or even sub-microscopic) level. The following illustration shows how various kink bands can develop.
The rock is mostly a micaceous metamorphic rock, probably formerly a shale. The heat and pressure of metamorphism converted the clays in the shale to micas (mostly muscovite I think). Probably late in the metamorphic episode, directed pressure squeezed the flexible layers of mostly mica to make these little folds.
Because the mica-rich layers are relatively incompetent, meaning they are not strong, and are not unified, coherent material, they react to stresses differently than something like a uniform thick limestone. It’s fairly likely that this rock was a relatively thin package of the fine mica layers, trapped between two stronger, more competent layers, and the fine mica-rich zone took up more of the deformation than the surrounding, stronger material.
The mica in the rock in the top photo gives the rock a fine satiny sheen, and as a field name we’d probably call this a phyllite, a rock with tiny, flat mica grains just large enough (and preferentially oriented) to create that reflective sheen, which varies depending on how the light hits it and the angle at which you are observing it. “Phyllite” is from a Greek word for “leaf,” alluding to the flat mica flakes stacked like piles of leaves (or pages in a book). If the rock were subjected to even higher temperatures and more pressure, the micas in the rock could grow larger and other chemicals might segregate into layers of other minerals, and then we’d probably call it a schist rather than a phyllite. As metamorphism proceeds and mineral crystals grow, mica grains might lose the details of their orientation that define these little folds, but even in a schist, mica grains are usually only sub-parallel, or only truly parallel to each other over short distances.
You can see the folds in the cross-section view, while the surface image shows the ripple-like effect of the multiple little fold crests about a millimeter apart. The specimen is about 5 cm from top to bottom in the photo.
The rock comes from the Gravelly Range south of Ennis, Montana. Fine-grained sediments, probably mud, were deposited as shale probably in Archean time (more than 2,500 million years ago). They were probably metamorphosed in the Big Sky Orogeny in early Proterozoic time, around 1.8 billion years ago, when the northwestern corner of the Wyoming Craton collided with other small continental blocks. The formation of the kink bands likely dates to that time as well, but it is possible that they formed in the much later flexing – folding and faulting – of the region during the Laramide-Sevier Orogeny about 90 to 55 million years ago. I collected it in 1989 or 1990.
Always wondered about these! Collected a bit of rock some decades ago, from the waste rock dumps of #3, Bathurst Mines, New Brunswick, that showed more pronounced small scale folding than I'd ever seen. First time the term "kink band" has come my way, but that is a perfect term for a piece of rock that looks like Medusa had taken umbrage at someone's kinky hair.
There was of course a highly regarded band called the Kinks in the mid to late 1960s. (And I think you can share a photo in comments by embedding a webpage with it on! Don't know any other way...) https://youtu.be/TYIl6n_SRCI?feature=shared