Visions in the Fog is a main quest in the Fallout 4 add-on .
the Children, the Sole Survivor can't just mosey up and ask. To do it, they need to pass a test and bring back a token of proof to Grand Zealot Richter.
Witness the debacle at the entrance to
The Nucleus and talk to Richter. Travel to
Atom's Spring and drink. Follow the
ghostly figure to the Children of Atom Shrine. Enter the little adjacent metal hut protected by ghouls.
Read the periodic table on the wall (or rather, the scrawls next to it) and use the terminal on the cage.
Mother Icon. Return to Richter.
Drink from the Spring
The Children of Atom require a ritual before allowing anyone into their sanctuary. Looks like I'll have to drink from a nearby spring. Bottom's up, I guess.
Follow the Figure
A ghostly woman beckoned me to follow her through the woods. Let's see where this goes...
Investigate the Holy Site
The ghostly figure directed me to a small holy site. Suppose I should check it out.
Unlock the Cache
This site appears to be some kind of shrine. And there's a strange carving locked away in a cage. I need to figure out how to get it open. Must be a clue around here...
Collect the Icon
I figured out the code to the terminal, "Mother." Now to unlock the cage and grab the carving.
Return to the Grand Zealot
The carving appears to be some sort of religious icon, maybe to this "Mother?" I should ask the Grand Zealot about it.
Turns out this "Mother" who led me through the woods was a messenger from Atom. Who knew? Now I can finally enter as an official Child of Atom.