Chapter 3: The World of Simple Programs

Section 5: Substitution Systems

Paperfolding sequences

The sequence of up and down creases in a strip of paper that is successively folded in half is given by a substitution system; after t steps the sequence turns out to be NestList[Join[#, {0}, Reverse[1 - #]]&, {0}, t]. The corresponding path (effectively obtained by making each crease a right angle) is shown below. (See page 189.)

From Stephen Wolfram: A New Kind of Science [citation]