I don't think it is anything so exciting, certainly not alien.
It is a pebble of concretionary nature.
That is, many rocks contain veins, of one arrangement or another. Where the veins are particularly concentrated and arranged, it may be a concretion of the sort called a septarian concretion or nodule. (There are other concretions that do not have the veining.)
If I am understanding your photos correctly, your particular pebble crosses the contact between two somewhat different fine-grained rock types, probably sedimentary. I suspect the blue side looks bluer in the photo than it really is (?). Veins with a pale blue colour are not common in sedimentary rocks (in metamorphic rocks there are several candidate minerals, such as kyanite). If I had to guess, I would choose celestine.