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Why was there such a massive use of dithering on the Super Nintendo?

This should be obvious, 256 is not a lot of colors. You needed dithering to create the illusion of more colors. As people have already mentioned, this works very effectively on CRT TVs of the day. If you didn't use dithering you would just have another problem: banding.

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This shit (the image on the left) is still a thing in a lot of games these days with day/night cycles. You can clearly see the "rims" of the changing light as the sun sets.

Unless it's just my tv or something, but I see it a lot.
 
Modern GPUs also lack easy, fast and memory efficient way to do order independent transperency.
Thus anything that is transparent needs to go trough different rendering pass or use dithering on fully opaque surface for easier rendering.

Pretty sure only hardware that did this properly was the gpu in dreamcast.
It did per pixel sort on all surfaces before rendering, thus not only did it handle transparency, but didnt render transparency behind opaque surfaces.

Not to mention we like to think with modern GPUs and displays that all visual spectrum is accounted for because we have so many colors or fancy HDR, but there are still limitations or heavy work required to over come. Inside doesn't get enough credit here, for example. While it got a lot of praise for its looks, more specifically all those dark gradients look incredibly smooth with no visual banding. At least none that I noticed. I have no idea how much work was involved in getting that all to look right but I doubt it was easy.
 
The interesting thing is that even though the SNES could theoretically display 256 colors at once (or more), the mode most games ran at (Mode 1) actually couldn't, which is most likely due to memory and performance reasons.

Mode 1, which is what most games used, can display three tile layers with two of them supporting 16 colors per tile and one of them (mainly used for text boxes and the HUD) supporting four colors per tile. Then there's sprites, of course, which also supported only 16 simultaneous colors maximum.

I think I read somewhere that Super Mario World and other early games mostly use 8 colors per tile in order to save space. Also, Donkey Kong Country uses programming trickery to display that smooth gradient, the graphics layer it is on doesn't support that many colors "out of the box".

Thanks for this answer.
 
Comes down to hardware design. Writing 256 color bitplanes is slower for one (more write ops), and if you also have multiple bitplanes for background and foreground then you most likely can't have both being 256 colours due to memory limits.

Not too familiar with SNES hardware but I've done some graphics programming for the Amiga computers and it's similar there. You can have a single 32 colour screen, or you can have two 16 colour screens for BG and FG. And same as SNES you can change the background colour during horizontal blank periods (actually every 8 pixels on the Amiga) to get smooth gradient effects - mostly useful for skylines and such.
 
The better question is why does FFXV still use dithering in 2016.

Tangential but Super Mario Odyssey also seems to use dithering in place of transparency for Mario when behind some types of objects, so it still has some modern uses beyond CRT blurring (optimisation? Sytlistic?) Bad quality examples (screenshots from youtube video)
Note that the pattern/resolution of the dithering seems to change depending on the wanted effect. (vine images taken in succession from [►]. Tostarena [►][►])
I wonder if they will keep that effect in the final release?

Edit: a Hat in Time also uses that. I guess it's more common than I imagined!
 
Not to mention we like to think with modern GPUs and displays that all visual spectrum is accounted for because we have so many colors or fancy HDR, but there are still limitations or heavy work required to over come. Inside doesn't get enough credit here, for example. While it got a lot of praise for its looks, more specifically all those dark gradients look incredibly smooth with no visual banding. At least none that I noticed. I have no idea how much work was involved in getting that all to look right but I doubt it was easy.
Indeed, inside is great example on how to use dither to make things look good in limited bitdepth of displays while making things faster at the same time.
https://www.gdcvault.com/play/1023002/Low-Complexity-High-Fidelity-INSIDE
http://www.loopit.dk/banding_in_games.pdf
 
Even Capcom's CPS2 arcade games use some degree of dithering. Color limitations were more stringent on pretty much all platforms throughout the 90's, mostly related to bit depth limitations in sub-palettes I suppose. Often noticeable on PS1 and PC games as well, with lots of visible banding on textures and such.
 
Tangential but Super Mario Odyssey also seems to use dithering in place of transparency for Mario when behind some types of objects, so it still has some modern uses beyond CRT blurring (optimisation? Sytlistic?) Bad quality examples (screenshots from youtube video)

Definitely optimisation, just drawing every other pixel of the "transparent" object is gonna be faster than calculating an alpha blend on each of them.

GTAV uses this technique too to fade in faraway object and make clipping less noticeable. The technical term for this is dithered / screen-door / stipple transparency.
 
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