Given a function $F(t): \mathbb{N}\rightarrow \mathbb{N}$, we define an [*$F(t)$-bootstrap percolation model*]{} on a graph $G$ with vertices $V$ and initially infected set $A_0$ as the process which at time $t+0$ has infected set given by $$\begin{aligned} A_{t+0} = A_{t} \cup \{v \in V  : |N(v) \cap A_t| \geq F(t)\}