I'm trying to create an an image in Illustrator which involves lines of colored boxes. There will be four rows, and the rows will be far apart on the left and come together on the right. I've created a rough impression using Photoshop's Liquify tool.

This of course looks horrible and I'm going for an effect in which the edges of the boxes stay aligned with the path rather than becoming parallelograms (as happened with Liquify). What's a way to do this in illustrator?
I have **more** ideas about what to do with these paths but I'm starting with the simplest version for learning purposes.
Mike