Crackle weave actually comes to us from Sweden, where it is called Jamtlandsväv. The term "crackle" was coined by Mary Atwater in the 1920s and 30s when she introduced it to her Shuttle-Craft Guild. The threading sequences for crackle weave patterns can be very long with no repeats, so be prepared for this if you want to make this towel.
The warp is 40/2 bleached linen, again set at 30 epi, and the ground weft is the same 40/2 bleached linen. For the pattern weft, I used 22/2 cottolin in autumn colors.
The treadling is shown in this screenshot from the weaving software I use (Fiberworks PCW). The patterned area is woven "using tabby", that is weave a pattern pick with the pattern colored yarn, then a plain weave pick, then another pattern pick, then the alternate tabby. Note that the center portion is not exactly symmetrical.