  Percolation on a one-dimensional lattice and fractals such as the Sierpinski
gasket is typically considered to be trivial because they percolate only at
full bond density. By dressing up such lattices with small-world bonds, a novel
percolation transition with explosive cluster growth can emerge at a nontrivial
critical point. There, the usual order parameter, describing the probability of
any node to be part of the largest cluster, jumps instantly to a finite value.
Here, we provide a simple example of this transition in form of a small-world
network consisting of a one-dimensional lattice combined with a hierarchy of
long-range bonds that reveals many features of the transition in a
mathematically rigorous manner.
