The last row of pictures below show a way to do this.

But is this somehow a special feature of cellular automata, or do other systems also have similar capabilities?

A combinator expression that corresponds to the operation of doing one step of rule 110 evolution.

Yet even so, there could still in principle exist in nature some other kind of system that would be able to do this.

But by the 1930s pure mathematics had already firmly defined itself to be based on the notion of doing proofs—and indeed for the most part continues to do so even today (see page 859 ).

Numbers that arise as solutions of polynomial equations are called algebraic; those that do not are called transcendental.  and π were proved to be transcendental in 1873 and 1882 respectively. … Note that the fact that a number is normal in one base does not imply anything about its normality in another base (unless the bases are related for example by both being powers of 2).

From the names of concepts and people that I mention, it is straightforward to do web or database searches that give a vastly more complete picture of available references than could possibly fit in a book of manageable size—or than could be created correctly without immense scholarship.

So-called robust statistics uses for example medians rather than means as an attempt to downplay outlying data that does not follow a Gaussian distribution.

Leading digits [in numbers] Even though in individual numbers generated by simple mathematical procedures all possible digits often appear to occur with equal frequency, leading digits in sequences of numbers typically do not.

But once again, while these strategies may in some cases lead to greater efficiency, they do not usually lead to qualitative differences.