Figure 1

(a) First four time steps of an IP dynamics in $d=1$. At the initial time step only the central throat is occupied (black). At each time step the occupied region (black) grows by invading the throat of the growth interface (gray) with the maximal capillarity. The growth interface is consequently updated by removing the just occupied throat and including the next unoccupied one in the direction of growth. (b) Tree representation of all the possible selection paths (i.e., realizations) of the task list dynamics or alternatively of IP in $d=1$. At each time step either the fresh new task ($N$) either the old one ($O$) is selected. Any possible dynamical history of length $t$ consists of a continuous sequence of arrows connecting the vertex at height $t=0$ with a node at height $t$.Reuse & Permissions

Figure 2

Waiting time distribution $P(\tau ,t_0)$ in the task list dynamics with $N=2$ and $p=1$ and initial time $t_0=0$, 10. Numerical data for each $t_0$ have been averaged over ${10}^7$ realizations. As shown, it is very well fitted by Eq. (9).Reuse & Permissions