Rubber mat to attach to 2x4s?

I'm convinced that there is a better material than carpet for attaching
to 2x4s for climbing. For example, I have a ribbed rubber doormat that
looks close if it were cut lengthwise and hot melt glued to the 2x4.
Something longer would be better. Some ribbed rubber mat, maybe
something used for exercise equipment area, or whatever. It doesn't have
to be cushy when it's used for climbing. It just has to provide traction
and hold up to the abuse of their claws without fraying and making a mess.

Thanks.