Quantum revivals are recurrent forms of wave packets  that, in the course of their evolution, return to their initial form after a certain "revival time". This Demonstration shows the propagation of a particle in a one-dimensional box of length 1 with Dirichlet boundary conditions. The coordinate runs on the horizontal axis and the vertical axis is . The probability density has interesting fractal properties  due to the wave function's self-interference resulting from the boundary conditions. Revivals of this type appear in many fields of physics.
The wave function can be represented by the infinite series
which is approximated by terms.
 M. V. Berry, I. Marzoli, and W. Schleich, "Quantum Carpets, Carpets of Light," Physics World, 14(6), 2001 pp. 39–44.
 M. V. Berry, "Quantum Fractals in Boxes," Journal of Physics: A Mathematical and General, 29, 1996 pp. 6617–6629. doi:10.1088/0305-4470/29/20/016.