Pixel density / color channel depth ratio for dithered gradients Dithering increases percieved color depth by adding a "noise" to an image on transform from high color depth (e.g. 32-bit floating point) to lower color depth (e.g. 8-bit integer). A prerequisite is pixel density being high enough for the brain to "blend" multiple pixels together. It is also dependent on viewing distance. I´m most interested in phone or desktop workstation distance. Dithering algorithm also matters but for the sake of the question lets assume it is "perfect".

RGB8 (TrueColor, 16 million colors) requires dithering for nice smooth gradients and tend to get really nice for your average monitor. RGB5 (HighColor, ~32k colors) requires dithering for gradients to look nearly smooth, but I think pixel density start to really matter at this point. I´m not sure if RGB4 (~4k colors) or R3G3B2 (256 colors) can ever have smooth gradients but given high enough pixel density it should be possible.

Is there any rule of thumb when it comes to pixel density / color channel depth ratio for a dithered image to appear having smooth gradients as percieved by the brain?
There has been quite some research into this using Barten contrast sensitivity function. It is the current formula behind the Dolby Perceptual Quantizer as featured in SMPTE 2084 and HDR10.

This, coupled with a colour appearance model such as the work behind Dr. Mark Fairchild's CIECAM02, can result in very accurate predictions of quantization depth.