Begin to introduce variations. Instead of one-up-and-one-down, change to two-up-and-two-down. This is still quite simple and can be accomplished by children.

Things become a notch more interesting when you use both patterns simultaneously:
    row 1: two-up-and-one-down
    row 2: two-down-and-one-up

A diagonal effect is seen when you offset the pattern in subsequent rows. Here:
    row 1: two-down-and-one-up
    row 2: same as above but offset it by one

Similar to the case above with checkerboard effect, the diagonal effect can be expanded to two-down-and-two-up.

Shown here are patterns with three-up (or three-down) combined with one-pdown (or one-up)

Really nice patterns can be achieved if you weave in and out in groups of 5. Note that the image on the right is the back side of the image on the left.

This pattern is the same as the one immediately above: namely, it has a diamond shape but with a dot in the middle.