Quartzite w/patterns!

Based on the appearance of the rock in the second image, it looks like it could be a type of polished agate or possibly a variety of chalcedony known as "plume agate" or "moss agate." These stones often have intricate patterns that resemble moss or plumes, which is similar to the pattern you see in the rock. The coloration and the inclusions within the stone suggest this type of mineral.