The "Q-curves" Q 1 (c) = c, Q 2 (c) = c 2 + c, . . . , Q n (c) = (Q n−1 (c)) 2 + c = f n c (0) have long been observed and studied as the shadowy curves which appear illusively -not explicitly drawnin the familiar orbit diagram of Myrberg's map f c (x) = x 2 + c. We illustrate that Q-curves also appear implicitly, for a different reason, in a computer-drawn bifurcation diagram of x 2 + c as well -by "bifurcation diagram" we mean the collection of all periodic points of f c (attracting, indifferent and repelling) -these collections form what we call "P -curves". We show Q-curves and P -curves intersect in one of two ways: At a superattracting periodic point on a P -curve, the infinite family of Q-curves which intersect there are all tangent to the P -curve. At a Misiurewicz point, no tangencies occur at these intersections; the slope of the P -curve is the fixed point of a linear system whose iterates give the slopes of the Q-curves.We also introduce some new phenomena associated with c sin x illustrating briefly how its two different families of Q-curves interact with P -curves.Our algorithm for finding and plotting all periodic points (up to any reasonable period) in the bifurcation diagram is reviewed in an Appendix.
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