Can we predict the future? This explorable contains a famous Cellular Automaton (CA): John Conway's "Game of Life". This is an excellent example of how even very simple model "rules" can yield complex behaviours when units interact spatially, making it hard to predict what will happen next.
This explorable was published in: Wortel & Textor. eLife 2021;10:e61288. doi:10.7554/eLife.61288.
Like Cellular Potts Models (CPMs), Cellular Automata (CAs) are discrete-space models that "live" on a grid; although CA cells typically occupy only a single grid point where CPMs describe cell shape at higher resolutions by letting cells occupy multiple, adjacent grid points. Still, just like in the CPM, the changes of the CA grid are defined by a set of rules.
The CA we will consider here is a relatively simple one called the Game of Life, designed in 1970s by mathematician John Conway. Conway wanted to build a Cellular Automaton that yielded "interesting" behaviours that are not easy to predict. He succeeded (as we'll see below). Nevertheless, the rules underlying these non-trivial outcomes are surprisingly simple:
That's it! You can see the rules in action below, where we always predict the change of the middle pixel:
Note that the Game of Life is deterministic: when we know the current state of the grid, we always know exactly what it will look like in the next step; there is no chance involved. Nevertheless, as we'll see below, the outcomes over time can be quite unpredictable...
As the Game of Life is deterministic, its outcome depends solely on the initial configuration of the grid. Nevertheless, it is not easy to predict from such an initial setting what its long-term outcome will be.
The Game of Life is quite rich in the types of patterns it allows, such as:
Below, you can explore the different types of patterns that occur in the Game of Life.
To conclude, here's an example with a larger grid, running at a somewhat faster pace:
Hit reset and try to predict what the end result will be. Can you?
Even a relatively simple model (with just a few deterministic rules) can produce complex behaviours and spatial patterns. Just imagine what that means for biology, where even the rules themselves already are complicated...