It has been limited the interest risen to analyze Rule 110, Santa Fe Institute offered a course for the analysis of Rule 110 in the summer of 2001.2 On the other hand Fred Lunnon has implemented an algorithm to obtain each one of the collisions among gliders of Rule 110. Recently Mirko Rahn formally discussed the operation of the cyclic tag system with regard of a Turing machine [33], the approach is implementing a function accepting some Turing machine and a configuration in Rule 110 which simulates the calculation of such a machine.
Rule 110 in spite of being an elementary cellular automaton, has an infinite universe and this is quickly comprehensible by the number of behaviors that can exist in the evolution space, collisions among gliders form a limitless data base, for example the B
, B, E and G gliders have a limitless number of collisions, without forgetting the grouping of gliders with or without extensions and the unlimited growth represented by the glider Gun, thus in this sense we have unlimited growth, insolubility and undecidable problems.
Another tool that offers many results is the cycle diagram described by Andrew Wuensche in [38] and [42], where the atractors cycles determine the periodic behavior for a sequence of certain length, the ancestor ramification illustrates the manifold for a given sequence and the leaves the configurations in the Garden of Eden. At the present time, Wuensche has found a very interesting cellular automaton with the same characteristics that the model of Conway and Cook in [43].
Other question in the case of the cyclic tag system is implementing some operations like the Fibonnaci sequence made by Paul Chapman (January 2003), the parenthesis balance, among other things.
Acknowledgements
In special to my professor Harold V. McIntosh and Department of Microcomputers in UAP. To Martin Schneider, Konrad Diwold and to Rule 110 Winter WorkShop by the hospitality and support, in special to Joana Margarida Simões for calculating new results. To Juan Carlos Seck Tuoh Mora by the aid and comments. This work was partially supported by CONACyT with registry number 139509.