This information is stored because each bounce generates a sustained
localized state of Faraday waves. The information being stored in waves, the data
about the trajectory are cumulated in an interference pattern due to the waves’ linear
superposition. Later, as the drop collides again with the interface, it ‘reads’ this
cumulated information and the local slope of the distorted surface determines the
direction and amplitude of the next jump. The dual nature of the walker is contained
in the path memory dynamics: the wave nature lies in the coding while the particle
nature lies in the reading. The reading can be seen as a local integration of the
wavepacket at a single localized point. It can be noted that a related situation has
been observed recently in crack propagations (Goldman, Livne & Fineberg 2010),
where waves emitted in the past can return to act on the propagating crack at later
times.