One other possible way to form the design without drawing all the connecting lines is to have a start pattern like this:



That is with additional lines drawn in, and the lines are extended slightly.

When arrayed, it results in this pattern:



Notice how the ends form a kind of "X" type crossing.

Here is a larger view:



When you have a set of curves like this that make a closed boundary with a bunch of little lines hanging off extra, you can use the boolean Union command on the curves to automatically trim away all the little excess lines for you and leave only the inside.

So selecting all those curves and running boolean union will create this:



However, it is a slightly different shaped design, all the lines are somewhat more rigid within each pattern piece. The other way of drawing connecting lines made those connection lines at a different slope which seemed a bit nicer to me.

- Michael