Self-matching bands in the paperfolding sequence
Bruce Bates, Martin W. Bunder, Keith P. Tognetti · Applicable Analysis and Discrete Mathematics · 2010
We compare term by term the paperfolding sequence with a copy displaced by d terms to obtain the matching fraction M (d). It is shown that M(d) has an interesting structure in that if d=2b(1+2s), then M(d)= |1-3/2b+1| thereby generating horizontal bands for each value of b. That is, M(d) depends only on b.