For Exercises 39–40, refer to the following. Step patterns are found in Celtic illuminated manuscripts, metalwork, and stone crosses. Square ones were constructed by first designing on a square lattice one- quarter of the pattern (say, the top right), using horizontal and diagonal lines to produce a prototype such as the following:

Then three copies were added, either by (1) rotating the original successively by 90° [as in accompanying illustration (a)], or else by (2) reflecting it across its right and bottom edges [as in illustration (b)]. (Based on research by Mark A. M. Lynch of Glasgow Caledonian University, Scotland.)