In order to illustrate my point, I will give the example of a well known mathematical construct, which is the cellular automaton. Basically, it's an infinite (or toroidal) space with N dimensions (usually N=2), composed of cells. If N = 2, it's like a grid (or a doughnut if you opt for the toroidal structure). Each cell can have a certain number of states (alive, dead, and you can add other states at will), and the next state of a cell depends on its own state and the states of its neighbors.
The Game of Life is the most well known example: a cell can be alive or dead. If an alive cell has two or three alive neighbors, it stays alive. If a dead cell has exactly three alive neighbors, it becomes alive. In all other cases, the cell dies or remains dead. What is interesting with cellular automata such as this, is that it is extremely difficult, if not impossible, to predict the final state of an initial configuration. You have to run a simulation in order to find out. Therefore, seeing it in action looks very much like random junk, and you would never think that complex structures could emerge from this. However, this is wrong. A simple structure, called the glider, can move across the plane diagonally. Other bigger structures can move horizontally or vertically. Structures can create beams of gliders. A prime number generator was made. And it was proven that it was possible to make a computer in the game of life. All of this out of awfully simple rules which someone came up with
on a trial and error basis. And to think there are two to the 512th power possible rules if N = 2, and 2 to the 2 to the 27th power if N = 3, that's quite a lot of possible rules for life (and we already know about awesome ones), and that's just one theory.