  In this paper, we compute categorical entropy of spherical twists. In
particular, we prove that Gromov-Yomdin type conjecture holds for spherical
twists. Moreover, we construct counterexamples of Gromov-Yomdin type conjecture
for K3 surfaces modifying Fan's construction for even higher dimensional
Calabi-Yau manifolds. The appendix, by Arend Bayer, shows non-emptyness of
complements of a number of spherical objects in the derived categories of K3
surfaces.
