I am looking for someone to explain how to achieve a subtle gradient in adobe illustrator like the one in this icon.
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It's hard to tell in your example, but it is common for apparently flat icons to gain that extra touch of polish by using subtle gradients.
To get it right you should work with tints and/or shades of a color to build your gradient. I find it easiest to work in the HSB model and carefully adjust the Saturation and Brightness values to step up or down on the gradient scale. You can also plug a base color in at 0to255.com to see a nice range of choices in hex.
In the sample below, you can see that there isn't a whole lot of room for steps between these two greens. The difference is just enough to give a little light affect to the small circle. The separation between the colors should be greater as the distance of your gradient increases.
Flat icons dont have a large amount of shadows, bevels and gradients. Study the icon and see what the user did.
For example take the green tag.
It is made up of what appears as 4 colors.
background: #8cb042 center area of tag: #a9c26f light area of fold: #b5d864 shadow area of fold: #b5d864
If there is a gradient or shadow it is very minamal to the normal eye (plus I cant examine it for fine detail at the image size). Dont over analyze something that isnt complicated. Maybe do some more searches and see the simplicity of flat icon design.
Check out this tutorial on Working with Gradients
It shows you how to manipulate the gradient tool to get the effect you want.
Excerpt from the link:
This will bring up another slider which you can click and drag on the center point and change the origin of the gradient. You can change the size by clicking on one of the points on the edge and dragging either way. You can also change the distance between colors by clicking on the integrated gradient slider.