It can be made denser than the one I made, but right now it's easy to wad it up and shove it in my 3 year old's pocket.
old bike inner tube
strong thread or embroidery floss
Step 1: Cut the tube
Slice some thin rings from the tube with the scissors. The outside edges will be slightly wider than the inside. That's fine.
Snip the rings open so they become strips.
You could certainly leave the loops uncut, but I don't trust my three year old to not try to stretch them around things he shouldn't. Strips are safer in our household.
Step 2: Form the base
Pull both ends of the string together so the strips form a tight circle. Pull tightly and tie, but don't snip the string. You'll notice that, due to the knot, some strips are closer together than other strips. Wrap the string tightly around the ball between strips that are close together to help space things out more evenly.
Step 3: Add sides
Repeat with a few more strips on the other side of the base. Find the tail of the string and use it to tie both ends tightly together.
Step 4: Fill in spaces and tie off
It's easy to catch even for those of us who are a little bit clumsy. This ball makes a great fiddling object for kids who crave tactile stimulation.