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Why does my Guassian blur in Illustrator go to gray or faded white when I use it?

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Anti-Aliasing in a CMYK document.

Using a 100% K black background...

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Using a Rich Black background...

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Working in RGB....

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CMYK documents have some limitations. Some of the raster options which rely on smooth color blends, or some blend modes, are more difficult to show on screen in CMYK. Illustrator has a difficult time previewing the combination of shapes. The reality is, on press, that black would be knocked out for the magenta. But Illustrator has difficulty showing the knockout smoothly due to on-screen anti-aliasing.

See here: Is CMYK mode not ideal for designs with blending mode?

With only 100%K for the black background, Illustrator is blending the CMY from x% to 0%, then making 0% transparent. So, you get anti-aliasing artifacts due to the range of the blend... i.e. 30% CMY blends to white, is anti-aliased, then white is set as transparent. Repeat for each stage of the blend to transparent. So only the black transition has an actual value range to blend. Anti-aliasing plays a huge role.

If you use a Rich Black then Illustrator has more than just K (black) to blend. It can blend x%C to the % of C in the background, then do the same for M and Y. This provides a smoother on screen appearance. Basically, with Rich Black you get a color to color blend as opposed to a color to transparent blend.

RGB follows the same logic as the Rich Black blending. You end up with a color to color blend to show the preview of the blur.

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This is because the black color you are using as a background.

In a CMYK file, the black from the Swatches palette is just 100% black:

black

Solution: change the background black for another black picked up from the Color Palette:

enter image description here

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