You need to make a tiling patter. There are a variety of ways to do this,
but the way I do it is:
create a bounding box a certain width. Let's say 1" wide x 4" tall
Draw a zebra stripe. Put it so that it overlaps the left side of the
bounding box. Now duplicate/offset this stripe 1" to the right. No fill in
the stripes in-between. Group the stripes, cut, and then paste inside the
bounding box. You now have a pattern that will tile horizontally seemlessly.
Group the pattern with the bounding box. Copy this and then past this as a
pattern inside whichever shape you want to have the pattern.