Hoi Pieter!
So exciting to hear that you're going to try replicate our bioprinter! Will this just be a one-evening event, or are you planning to work on this over a longer period of time? If you only have the one evening, then just getting all the hardware assembled, wired up and working will probably take up all your time.
Implementing Conway's Game of Life would be really cool, but very challenging. Basically you'd have to start with a significant synthetic biology project, genetically engineering the cells to be printed such that they emit some short-range diffusible signal, and then engineer some logic into the cells so they respond to that signal in a very non-linear fashion that mimics Conway's rules. Doing all that would likely take several months even for a competent academic team. And then you haven't even started printing yet...
An easier project along the same lines would be to engineer two strains of E. coli to implement a negative feedback loop: strain A produces a diffusible signal that turns ON strain B, and strain B produces a diffusible signal that turns OFF strain A. Then watch the interesting spatial patterns develop. See if you can tune the parameters to generate various animal coat patterns: zebra, leopard, giraffe, etc.
There's a bunch of real scientific research questions you could try to address with a bioprinter like this as well: isolate some cross-feeding microorganisms that seem to crossfeed metabolites between each other, and print them at different distances and in different spatial arrangements with respect to each other.
One big limitation of our current bioprinter is that you can only print with one "ink" at a time. That is why we are currently working on replacing the inkjet print head with a couple of syringe pumps. That should open up a whole other range of applications as well.
Patrik