To have some 3D population of bacteria build structures with certain (stochastic?) patterns/regularities.
Quorum sensing and some fancy cascades triggered when some threshold is reached, leading to the excretion of substances that will add up to structures (or some other interesting phenomena).
The Random Sphere approach
Assume the bacteria population starts with the slow but steady production of A, which diffuses into the vicinity and can be sensed by other bacteria (Quorum Sensing). When a critical threshold is reached within a bacterium, a cascade is triggered (nothing new there). The cascade consists of a short but intensive production of B and a delayed aptosis (suicide). It is very likely, that the process is stochastic, i.e. that due to differences in individual sensitivity and in local concentration some bacteria will be first, while others will never sense a critical threshold of A and thus never start the cascade. Probably, A and B will both need to degrade rather quickly. While A now is no longer produced around the bacteria in the death cascade, B is suddenly present in hopefully high concentrations in its vicinity. The survivors in the vicinity that have not reached the threshold of A to trigger a cascade themselves, will now react to B and start to excrete some substance C, which will harden to some structure that will most likely form spheres or some very porous structure.
This is an idea I had during the discussion yesterday with Jonas. I have not totally thought this through. The dynamics are not entirely trivial, I guess, especially if not tuned well. And I obviously have no clue about what is really possible biologically speaking, especially with the excretion of structures.