Boolean model
I've provided a small interactive tool which lets you play with the parameters of the Boolean model inside a disc. The tool is available here.
It includes several regimes (the "thermodynamic" and "connectivity" regimes) in which interested events are known to occur. Inside the thermodynamic regime, a unique giant component emerges (around t=1). Inside the connectivity regime, in which the radii are much larger than the thermodynamic regime, the last few isolated points and small clusters are connected to the giant component. Later in the connectivity regime, the whole disc is covered.
A button at the bottom allows you to colour the clusters by their number of discs, which is especially useful in the thermodynamic regime to see the emergence of a giant component. Warning: it's a bit slow when there are a lot of discs.
Another button replaces the discs by pumpkins (best enjoyed around Halloween).
Johnson-Mehl tessellation
An interactive simulation of the Johnson-Mehl tessellation (made in PyScript) is available here.