The Realm of Dream was originally planned to be OmniPark's 8th Realm, but was scrapped before construction on the park began in 1975.
Development of the Realm proceeded well into the design stage, with Technosophers Beth Bachmeier and Elijah Shattuck producing numerous sketches and concept art pieces (very few of which have survived). However, park CEO Dalton Teague personally terminated the project in 1975, before engineering could begin. Teague never provided an explanation for this abrupt decision, aside from the terse and cryptic statement that "OmniPark has seven Realms." 
Since the Realm of Dream's attractions were never fully storyboarded, little is known of their themes and storylines, or even how they were intended to behave. Bachmeier's concept art and Shattuck's notes and sketches provide some clues, but these are fragmentary.
Realm Layout and Design
The design team of Bachmeier and Shattuck envisioned the Realm of Dream as a descending spiral, symbolizing the mind's descent into deeper stages of sleep. As park guests followed the spiral farther underground, the lighting was to grow dimmer, and fleeting images of "dreams" were to be projected with increasing vibrancy — until, at the level of "Deep Sleep," guests would be entirely surrounded by vivid dream imagery swirling across the walls, floors and ceilings.
Shattuck's notes include a mention of a "technology" that would "evoke a lucid dream state while guests are awake," as they passed through the Realm's entry portal. It's unknown how this "technology" was intended to function, or whether OmniPark engineers were actually tasked with developing it, or if it was even physically plausible — or simply another of Shattuck's unorthodox ideas.
Upon entering the Realm, guests would have the choice between dining at an "Imaginary Snacks Cafe," or proceeding directly to the first attraction, which was working-titled "REM Wonderland."
Attraction: REM Wonderland
Shattuck's notes describe this attraction as "An OmniVision voyage through the familiar territory of ordinary dreams" — implying that it would have utilized a room-encompassing OmniVision rear-projection system similar to the one used in the Realm of the Stars's Nebula Quest attraction. Sketches indicate that guests would have been seated in a theater in groups of 30. Beyond this, little is known about Wonderland's plot or mechanics.
Attraction: Into the Chasms of Sleep
This attraction was apparently intended to simulate the actual psycho-physical experience of falling asleep. According to Shattuck's notes, guests would be seated in a theater that also functioned as a large ride vehicle, moving guests into a "cycle chamber" that would "simulate freefall." This would presumably be accompanied by visuals and music — though, again, Shattuck's notes are unclear about the ride's storyline.
Attraction: Deep Sleep
Shattuck's notes and Bachmeier's concept art indicate that this attraction was to be a standard "dark ride," at least in engineering terms: ride vehicles would proceed through a series of scenes depicting "a voyage through the shared realm of the collective unconscious." Based on OmniPark's other dark rides, these scenes would presumably have included animatronic figures, visual effects, music, and perhaps even tactile effects like those used in The Realm of Man's attraction The Story of Man. However, the ride's intended plot remains unknown.