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Consider the hypergraph bootstrap percolation process in which, given a fixed$r$-uniform hypergraph $H$ and starting with a given hypergraph $G_0$, at eachstep we add to $G_0$ all edges that create a new copy of $H$. We are interestedin maximising the number of steps that this process takes before it stabilises.For the case where $H=K_{r+1}^{(r)}$ with $r\geq3$, we provide a newconstruction for $G_0$ that shows that the number of steps of this process canbe of order $\Theta(n^r)$. This answers a recent question of Noel andRanganathan. To demonstrate that different running times can occur, we alsoprove that, if $H$ is $K_4^{(3)}$ minus an edge, then the maximum possiblerunning time is $2n-\lfloor \log_2(n-2)\rfloor-6$. However, if $H$ is$K_5^{(3)}$ minus an edge, then the process can run for $\Theta(n^3)$ steps.

Long running times for hypergraph bootstrap percolation