I'm experimenting with "Tapestry Crochet," and perhaps the technique might work for your application.

Here's a basket pattern from a lady who does tapestry crochet, and has written several books on the topic:

http://iweb.tntech.edu/cventura/basket.html

This is just a small basket, but there is no reason you cannot just use larger hooks to adjust for the larger size of the fabric strips, and add increases in the right places to change the shape.

You might have to make up your own pattern, or perhaps there'll be one in Carol Ventura's books that is already the right shape.

Here are her basic instructions on tapestry crochet:

http://iweb.tntech.edu/cventura/rightstitches.html

She doesn't tell how to get started, but it's just regular cast-on with a chain stitch and single crochet until the first time you need to change colors.

When making a basket, the stitches need to be very tight, with only tiny holes between the stitches. The tapestry crochet technique of covering over the alternate color yarn tends to make a stiffer fabric--perfect for a basket.

Another place to look is on the UrbanSpinner blog:

http://www.urbanspinner.com/blog/archives/000160.html

The Native American baskets look more like something a cat might like to sleep in. I think your cats are going to love the fabric baskets. Anything that is fuzzy or holds their heat is wonderful for them.

Another idea for a pattern that might work: Some people recycle strips of plastic shopping bag to make a tote. You use an N hook, and it makes a very stable fabric from the plastic. The diameter of the plastic strips is very similar to the fabric strips you'll be using.

Hopes this gives you some ideas!

MaryLiz

Thanks! These sites were even better than I had imagined.