  Inspired by the works of Goldreich and Ron (J. ACM, 2017) and Nakar and Ron
(ICALP, 2021), we initiate the study of property testing in dynamic
environments with arbitrary topologies. Our focus is on the simplest
non-trivial rule that can be tested, which corresponds to the 1-BP rule of
bootstrap percolation and models a simple spreading behavior: Every "infected"
node stays infected forever, and each "healthy" node becomes infected if and
only if it has at least one infected neighbor. We show various results for both
the case where we test a single time step of evolution and where the evolution
spans several time steps. In the first, we show that the worst-case query
complexity is $O(\Delta/\varepsilon)$ or $\tilde{O}(\sqrt{n}/\varepsilon)$
(whichever is smaller), where $\Delta$ and $n$ are the maximum degree of a node
and number of vertices, respectively, in the underlying graph, and we also show
lower bounds for both one- and two-sided error testers that match our upper
bounds up to $\Delta = o(\sqrt{n})$ and $\Delta = O(n^{1/3})$, respectively. In
the second setting of testing the environment over $T$ time steps, we show
upper bounds of $O(\Delta^{T-1}/\varepsilon T)$ and $\tilde{O}(|E|/\varepsilon
T)$, where $E$ is the set of edges of the underlying graph. All of our
algorithms are one-sided error, and all of them are also time-conforming and
non-adaptive, with the single exception of the more complex
$\tilde{O}(\sqrt{n}/\varepsilon)$-query tester for the case $T = 2$.
