The Land of Thought and Flow (abbreviated as LOTAF) is Terezi Pyrope's planet in the Medium. The sky appears to be made of enormous neurons flashing with impulses. The symbol for Mind resembles one of the stylized neurons as they are seen in the sky here. The landscape is covered in hills and ruins that resemble Roman Courthouses. Rivers flow throughout the land, over hills and through ruins.
The underlings of this planet are composed of grist that is dark red (carmine) in color, possibly the same substance that the planet's rivers flow with. One of the largest monsters so far has been seen roaming this planet.
Judging by the statues Terezi draws on, and her familiarity with them, the Consorts of this land are likely Crocodiles.
Terezi spent some time exploring her planet alone until she was joined by Karkat Vantas. Karkat then left to the next planet as Terezi stayed behind. She was then contacted by her exile.
LOTAF was destroyed with the other eleven planets when Jack Noir rampaged through the troll session.