Biological evolution is an example of an informal process of development, showing that such processes are actually possible in the physical world. There is certainly no single formal theory that describes how all the different genes and organisms it generated came into being. In an organism, there are some processes that are under the control of the genes. These processes represent the normal functioning of the organism. But there are always some processes that are not under the control of the genes.
For example, if you look at what is going on in a cell, e.g. in a single-celled organism, you will notice that some of the processes happening there, like some of the movements of organelles in the cell’s plasma, are clearly random. They are not under the direct control off the cell’s genes. Likewise, the molecules in the cells move and react in ways not dependent of the control of the genes.
In particular, mutations of the organism’s genes themselves are not under the genome’s control. There might be some controlled processes of gene editing, like crossing over between chromosomes etc. But generally, the processes changing the genes are not controlled. And this is important. If all mutations were completely controlled, the evolutionary potential of the organism would be limited to information already contained within its genome. All “evolution” in such an organism would actually be an instance of ontogenesis, as opposed to phylogenesis, and the organism could actually not develop into anything new. It would not be evolving in the sense the word is normally understood.
To use a concept from computer science here, we could say that an organism is “emulated”by a physical system. Some of the properties of the physical system “running” the organism are under the control of the organism’s genome, while others are not. The description of the organism as a gene-controlled system is incomplete with respect to the physical system. The physical system has more properties than the genome describes. There is a “residuum” of properties or processes outside of the control of the genome. Moreover, the organism is in constant exchange with its surroundings. Mutations act out of this residual part of the system and out of the environment.
The controlled part of an organism might be described in terms of a formal theory (simulations exist already for simple organism, like some bacteria, and scientists are working on simulations of some simple animals, like nematodes). But such models are incomplete in the sense that they fail to describe the potential of the organism to evolve. Evolution is an informal process. And while some processes of evolution may be modelled inside a computer, true, open-ended evolution cannot be described in terms of an algorithm alone. It is an informal process that would need a non-algorithmic source of true randomness.
An organism like the Paramecium you can watch in the film will, most of the time, behave according to the normal way of its species, but there is the potential to evolve into something else. The bilaterian animals to which we belong developed from simpler animals like sponges that in turn developed from single-celled organisms (a kind of flagellate). And these developed out of even simpler organisms. A complete description of these simple, single celled ancestors would have to include all the organisms they could evolve into, including you and me.
(The picture is from https://commons.wikimedia.org/wiki/File:Salpingoeca_sp..jpg. It shows an electron-microscopic image of a choanoflagellate. This group of single-celled organisms is thought to be closely related to animals and fungi. The film, on the other hand, shows a Paramecium, a cilliate only distantly related to animals.)