One area of interest in terms [Cellular automata and the emergence of complexity]of studying the emergence of irreducible phenomena can be found at http://www.wolframscience.com by Steven Wolfram. Also this is a brief summary pdf file: http://www.wolframscience.com/reference/CAandNature.pdf Also related (taken from this site) are some of the work that Paul Davies' work on astrobiology has led him to "wonder whether perhaps living systems might be characterized by having rules that somehow depend on global features of their state." Below are some 'quick takes on some of the ideas and discoveries' in this area: 1.  Mathematical equations do not capture many of nature’s most essential mechanisms. 2.  Thinking in terms of programs rather than equations opens up a new kind of science. 3.  Even extremely simple programs can produce behavior of immense complexity. 4.  Simple programs can yield behavior startlingly like what we see in nature. 5.  Simple programs can do much more than typical programs written by programmers. 6.  Simple computer experiments reveal a vast world of new phenomena. 7.  Randomness in physics can be explained by mechanisms of simple programs. 8.  Thermodynamic behavior can be explained by mechanisms of simple programs. 9.  Complexity in biology can be explained by mechanisms of simple programs. 10.  Simple programs may lay the groundwork for new insights about financial systems. 11.  Our whole universe may be governed by a single underlying simple program. 12.  Underlying space there may be a simple discrete structure. 13.  Time may have a fundamentally different nature from space. 14.  Systems with exceptionally simple rules can be universal computers. 15.  Many systems in nature are capable of universal computation. 16.  The Principle of Computational Equivalence provides a broad synthesis. 17.  Many systems in nature are computationally equivalent to us as humans. 18.  Many systems in nature can show features like intelligence. 19.  Extraterrestrial intelligence is inevitably difficult to define and recognize. 20.  It is easy to make randomness that we cannot decode. 21.  Apparent complexity in nature follows from computational equivalence. 22.  Many important phenomena are computationally irreducible. 23.  Apparent free will can arise from computational irreducibility. 24.  Undecidability occurs in natural science, not just mathematics. 25.  The difficulty of doing mathematics reflects computational irreducibility. 26.  Existing mathematics covers only a tiny fraction of all possibilities. 27.  Studying simple programs can form a basis for technical education. 28.  Mechanisms from simple programs suggest new kinds of technology. Further explanations can be found here: http://www.wolframscience.com/reference/quick_takes.html Best, GSM