It is known that biosystems can be modelled by cellular automata (CA). Cellular automata are regular structures in an N-dimensional space which are composed of finite size cells that each can be in one of a number of states. There are also a number of rules specified for state transitions. John von Neumann showed that there exist cellular automata capable of modelling biosystems. These automata are dynamically stable, self-replicating and Turing-equivalent (i.e. they are in fact a universal computer).

Interestingly, in the configuration spaces of biosystems there can be isolated functional zones amid chaos. When you think of this, this is actually expected because in reality a complex enough functional system is bound to have zones of function-compatible parameter values. The relative size of such a zone tends to be smaller as the number of parameters and their value criticality for normal operation of the system grow. The same holds for biomachines even taking into consideration their high adaptability. This is what undermines both classical Darwinism and the synthetic evolution. If two given taxa belong to two separate parameter zones, there is no selectable Darwinian path from one to the other.

Earlier we discussed the options for the blind Darwinian search in a configuration space. Here is another very interesting paper on the possibility of reaching target zones by Darwinian means (mutations + drift + natural selection) [Bartlett 2008], which summarises the results of mathematical modelling of the evolution of biosystems using cellular automata. 4 complexity classes of CAs have been identified:

Interestingly, in the configuration spaces of biosystems there can be isolated functional zones amid chaos. When you think of this, this is actually expected because in reality a complex enough functional system is bound to have zones of function-compatible parameter values. The relative size of such a zone tends to be smaller as the number of parameters and their value criticality for normal operation of the system grow. The same holds for biomachines even taking into consideration their high adaptability. This is what undermines both classical Darwinism and the synthetic evolution. If two given taxa belong to two separate parameter zones, there is no selectable Darwinian path from one to the other.

Earlier we discussed the options for the blind Darwinian search in a configuration space. Here is another very interesting paper on the possibility of reaching target zones by Darwinian means (mutations + drift + natural selection) [Bartlett 2008], which summarises the results of mathematical modelling of the evolution of biosystems using cellular automata. 4 complexity classes of CAs have been identified:

- automata that always arrive at a homogenous state no matter what their initial state was;
- automata that have a finite sphere of influence for outcomes even if the computation was carried out an infinite number of steps;
- chaotic systems, where initial states do not have either a bounded sphere of influence nor do they produce predictable results. However, they do have stable statistical properties;
- automata that exhibit a hybrid of both the periodic behavior of Class 2 systems and the chaotic nature of Class 3 systems. More importantly, they are unpredictable both in their exact outcomes as well as well as in their statistical properties. These CAs are Turing-equivalent.

Since class 4 systems are chaotic to some degree, the mapping between changes in code and changes in the outcome (genotype-phenotype correlation) is also chaotic. Consequenly, in this case a Darwinian selectable path from one taxon to another does not exist.

An interesting property of class 4 automata is the dependence of the degree of chaotisation and of evolvability on the implementation language. Phenomena similar to irreducible complexity [Behe 1996] are, as a matter of fact, not invariant with respect to the implementation language. According to Bartlett, the existence of irreducible complexity and similar phenomena points to the existence of a higher order genome evolution control. Notwithstanding the evolvability of feedback loops, as Bartlett points, they must be initially loaded into biosystems, since feedback loops never arise spontaneously in reality. In conclusion, we just point out that the presence of control over evolutionary processes is, in some sense, the demise of evolution per se (never mind the inevitable oxymoronic phrase "evolutionary process") [Abel 2011], since evolution by definition is undirected.

An interesting property of class 4 automata is the dependence of the degree of chaotisation and of evolvability on the implementation language. Phenomena similar to irreducible complexity [Behe 1996] are, as a matter of fact, not invariant with respect to the implementation language. According to Bartlett, the existence of irreducible complexity and similar phenomena points to the existence of a higher order genome evolution control. Notwithstanding the evolvability of feedback loops, as Bartlett points, they must be initially loaded into biosystems, since feedback loops never arise spontaneously in reality. In conclusion, we just point out that the presence of control over evolutionary processes is, in some sense, the demise of evolution per se (never mind the inevitable oxymoronic phrase "evolutionary process") [Abel 2011], since evolution by definition is undirected.

**References**

**David Abel (2011)**: The First Gene.**Jonathan Bartlett (2008)**: Wolfram's Complexity Classes, Relative Evolvability, Irreducible Complexity, and Domain-Specific Languages. Occasional Papers of the BSG 11:5.**Michael Behe (1996)**: Darwin's Blackbox.