If you know for sure that it's Dinantian, that makes an explanation even easier.
Whereas sedimentary layers are generally laid down horizontally and then lithified (squeezed, baked and turned to rock), not all rocks preserve a perfect stratified form.
In the Carboniferous period, the centre of Scotland was essentially a large rift valley, a descending mass of crust between two even bigger masses of crust that were separating slowly. The land to the north, currently the highlands, was a source of sediments. The land to the south, currently the southern uplands, was also a source of sediments. However, the main character of the central lowlands was that it was at sea level. For a while it would be just below sea level and would have been rich with life, particularly coral reefs and silty lakes or seas where sealife debris like shells and reefs that were very calcium rich resulted in limestones. As these areas bult up to sea level, they became choked with silt and sand, giving us mudstones, sandstones and siltstones. Some of these yield fossils of bivalves. In time, the area would become stably terrestrial and would have been characterised by swamps with primitive plants and trees. These are the source of scotland's coals.
But back to that rift valley. With an intermittent, juddering descent of the central block downward, the areas of 'land' were periodically submerged and became shallow seas. After a dump of new sediment, the area again teemed with marine life, and the commencement of the next layer of future limestone was underway.
This happened in the scottish lowlands cyclically many many times. A look at the stratigraphic record shows a more or less perfect conformable cycle of limestones, sandstones, coal measures, thin sediments, limestones, sandstones, coal measures etc.
So in this context you need to think of recently disturbed sediments, still in a quasi-liquid state, being subjected regularly to earthquakes that were probably on a San Andreas Fault scale. The central lowlands is riddled with smaller faults too, what is known as syndepositional faulting that happened during rather than after sedimentation. Local topography would result in underwater and terrestrial landslides. But you can often find an even simpler phenomenon in scottish carboniferous rocks called 'dewatering structures'. This is where the otherwise clean planar structure of the sediments has been bent, billowed, slumped, folded or sheared, while the sediments were still soft.
On the Fife coast in carboniferous rocks I have seen almost spherical plumes of rocks which have been cut through by weathering to give concentric circles. Maybe you are seeing something similar, i.e. lamina distorted before lithification.