Tapered checkered pattern conundrum

Question

I've been tasked to create this wavy checkered pattern design by a client. He liked the design, but he wanted the pattern to continue and taper off on both sides. The problem is, I've figured out how to do it on one side using warp flag option on a compound checkered object, but I have no idea how to create the same pattern on both sides in a passable and reasonably simple way.
 
I'll include an image showing what I mean.
 
Have any suggestions?

[ attachment inserted as inline image by moderator ]

Myra Ferguson · Accepted Answer

It looks like you made a shape and filled it with a pattern fill. See step #3 for turning your pattern into something you can use to make a brush or the alternate approach to making the pattern. Either way, you need to have just the shapes to be able to turn them into a brush. Then do #4 to make an Art brush.

Myra Ferguson · Answer

If I understand what you want, you can make an art brush with the checkered pattern, draw the curve, and adjust the width at each end.

Draw a square with the Rectangle Tool and fill it with black
Copy the square, drag it next to the first one, and fill it with white
Make copies to create the pattern for however many repetitions you want (You can do it by making a pattern, filling a rectangle with the pattern, releasing the clipping mask, ungrouping, and deleting the parts you don't want)
Drag the checkered arrangement of squares to the Brushes panel and create a new Art brush
Draw the curve how you want it
With the curve selected, click on the brush to apply it
Select the Width tool (Shift + W)
Click on on one of the ends of the curve and drag it inward to taper the end
Repeat on the other end

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