Another model based on cellular automata, taking into account a simpler replicating network of continuously mutating parasites and their interactions with one replicase species, was proposed by Takeuchi and Hogeweg and exhibited an emergent travelling wave pattern. Surprisingly, travelling waves not only proved to be stable against moderately strong parasites, if the parasites' mutation rate is not too high, but the emergent pattern itself was generated as a result of interactions between parasites and replicase species. The same technique was used to model systems that include formation of complexes. Finally, hypercycle simulation extending to three dimensions showed the emergence of the three-dimensional analogue of a spiral wave, namely, the scroll wave. Comparison with other theories of life The hypercycle is just one of several current theories of life, including the chemoton of Tibor Gánti, the (M,R) systems of Robert Rosen, autopoiesis (or self-building) of Humberto Maturana and Francisco Varela, and the autocatalytic sets of Stuart Kauffman, similar to an earlier proposal by Freeman Dyson. All of these (including the hypercycle) found their original inspiration in Erwin Schrödinger's book What is Life? but at first they appear to have little in common with one another, largely because the authors did not communicate with one another, and none of them made any reference in their principal publications to any of the other theories. Nonetheless, there are more similarities than may be obvious at first sight, for example between Gánti and Rosen. Until recently there have been almost no attempts to compare the different theories and discuss them together. Last Universal Common Ancestor (LUCA) Some authors equate models of the origin of life with LUCA, the Last Universal Common Ancestor of all extant life. This is a serious error resulting from failure to recognize that L refers to the last common ancestor, not to the first ancestor, which is much older: a large amount of evolution occurred before the appearance of LUCA. Gill and Forterre expressed the essential point as follows: LUCA should not be confused with the first cell, but was the product of a long period of evolution. Being the "last" means that LUCA was preceded by a long succession of older "ancestors." References External links J. Padgett's Hypercycle model implemented in repast Origin of life Self-organization