Sampling Artifacts

Sampling from a 3d-noise-map doing ray-marching in a fragment-shader I ran into strange noisy artifacts when zooming in. Are those simply because the noise-map’s resolution isn’t high enough? When zooming in even further there are patterns like this. The noise map has a quite low resolution of pow(64, 3) but should be smooth.

I tried increasing the Resolution of the map - which look better: no question… But those Patterns remain. Can those be caused by numerical instability of the ray-intersection function?

I could nearly fix this by using a highp-precision qualifier. The strange thing is this seems to be caused by a quite simple calculation:
Delta = (scalar1 - scalar2) / 4.0
and not by the intersection-routine itself which is quite more complicated. That’s something I would never have expected.