Knopp function K(x) makes use of two parameters a and b. The authors study the set of x where K takes its maximum value. A simple efficient algorithm makes possible the computation of any maximum point. The authors then analyze the variations of maximum points when a increases from 0 to 1 by using a bifurcation diagram. If b is an even integer and if , the maximum on is uniquely taken at . If b is an even integer and if , then the discontinuities in the bifurcation diagram are easily explained. A close connection between left-hand limits in this diagram and the Thue-Morse sequence is found.
