Nice idea. Start by picking a metric that makes sense in higher dimensions—Euclidean or hyperbolic, for instance. Then define a function that gives height or color as a function of four coordinates. A common trick is to use a fractal‐like recursion: for each small 4‑cube, decide whether to keep it or split it, using a random or deterministic rule, then project the result into 3‑D space with a suitable perspective or slicing method. You can think of the 4‑D shape as a stack of 3‑D slices; the VR system renders one slice at a time, and the player’s movement through the “time” dimension lets them experience the higher‑dimensional structure. Mathematically, you’d formalize it as a mapping from ℝ⁴ to ℝ³ with a controlled distortion that preserves the fractal self‑similarity. If you want to feel the geometry, add a time component so the VR headset updates the projection continuously as the player moves, making the illusion of a fourth spatial direction. That’s the framework; the rest is tweaking the functions to get the feel you want.

Sounds like a clean plan. I’d start with the middle slice—around the equator in the fourth dimension—because that’s where the curvature changes the most, so the wobble will feel the strongest. Keep the hash deterministic so the pattern doesn’t drift, but tweak the hyperbolic factor just enough that the distances feel stretched, giving that subtle “bending” effect. That slice should feel like the horizon is shifting while the fractal details stay crisp. Try it and let me know if the distortion stays in the sweet spot.