As of Version 0.05a, wallpapers have been added to Uneven Dream, viewable on both Kubotsuki's and Totsutsuki's PCs. Both characters share the same set. There are currently 17 wallpapers to unlock plus a custom slot to insert the player's own wallpaper. Below is a gallery of all of them and their unlocking conditions.
Custom wallpaper slot. Instructions for replacing this wallpaper are written on it.
"Factory Default" by FD.
Default wallpaper for both characters.
"Design K" By ZLD.
Available from the start.
"Design T" by ZLD.
Available from the start.
"A Trip to Metal World" by 001247.
Interact with the large fleshy trees in Metal Mounds until the panorama changes for a second.
"Bad Joke" by gummyshark.
Enter the innermost room in the Clownpieces.
"Mysterious Mime" by gummyshark.
Find and interact with both Mimes in the Metal Mounds
"Breeze" by Jojogape.
Find and obtain Totsutsuki's Cape effect.
"Angel" by EBRoxas72.
Enter the Angel Room in Purple Town
"My dreams so far..." by peppe_ykoba.
Find and obtain the following Totsutsuki effects: Sunflower, Star, Music Box, Cape, UV Light, and Nightcap.
"See, it's a crane!!" by gummyshark.
Obtain the Origami effect and use its Shift action (due to an oversight some situations can make this wallpaper unobtainable currently).
"...Someday I'll learn" by Ebraxas72.
Visit the Peeper Room in Winter Village.
"Dreaming Parallel" by gummyshark.
Play Uneven Dream for 30 minutes (not counting time the menu is open).
"Chased" by EBRoxas72.
Get caught by both types of chasers currently in the game.
"Winter Dawn" by EBRoxas72.
Sit on what's depicted in the wallpaper in the Winter Village
"The Showroom" by sniperbob.
Enter the Sandy Showroom for the first time.
"Handicraft" by CrystalCreation.
Obtain 5 effects for each character.
"Pyrotechnician Dreamers" by EBRoxas72.
See both the Turtle Hole and Origami Flight events.