

Start out with a blank canvas, and create a black circle.

With your circle selected, apply the transform effect (Effect > Distort & Transform > Transform...).

Use the following values. Don't forget to check the Preview box to see the changes in real time. You might have to adjust the Horizontal value according to the original size of your circle.

Make sure the first circle is selected (the other circles are just copies, so you cannot select or modify them) and display the appearance palette, then select the element's fill.
One word of warning: the appearance palette will always display the appearance of the last element selected, even when that element is not selected anymore. This means that whenever you're using the appearance palette you need to make sure the element you want to modify is selected, otherwise you might just be changing empty settings.

With the fill selected, apply a linear gradient.

With your circle selected, move the transform effect's layer to the top. Moving layers around changes the order in which effects are applied, and which particular elements (the fill, the stroke, both, etc.) they are applied to. In this case, we want our gradient fill to be applied after the transformation, so we put the transform layer first.

This is what you should get.

Now apply a second transform effect. Illustrator might ask you if you want to apply a second effect or edit the first one. We want another one, so choose that option. This time, we will not touch the scale or move sliders, but instead we will add a 30° rotation, with 11 copies (enough to make a full circle, since 12*30=360 (the original plus 11 copies). Be sure to specify the center of the rotation as the left middle point.

Time for another effect. This time let's add a 75% Fisheye Warp (Effect > Warp > Fisheye).

Once again the default layer order is not appropriate. We want the warp to effect the object as a whole, not each individual circles. So let's move the Warp layer all the way down.

You should get something like this

This tutorial makes me so happy I could just dance ! Let's do the twist: Effect > Warp > Twist.

Now we add another Twist, as we did in the previous Step. This is the moment where you can experiment with different effects until you get what you want.

Here's the finished product. Now I know what you're thinking. Nothing special, right? Let me show you something.

Since we used effects for everything, we can use our nice spiral thingy to make a style. Just drag the whole thing to the Graphic Styles palette. Now create a black rectangle elsewhere on your canvas, and apply the style to it (to do this, just select the rectangle and click on the style in the graphic styles palette). What do you get?

And that's just the beginning. Once you're happy with the shape, you can expand the object's appearance (Object > Expand Appearance). Next, add other effects, like 3D rotation, and tweak the colors.
