This result can be seen in three fundamental parts, first in determining the system that must model a Turing machine [34], this model is represented as a variant of the tag system [28], [36], [37] and [29], the cyclic tag system [7]. The problem of deciding when a machine must stop in a tag system is the problem of the word correspondence proposed by Emil L. Post [31].
The second part is modeling the mechanism with the gliders of Rule 110, this is obtained handling well-defined blocks of gliders settling down a data area and another area of operations, implementing the basic operations of a tag system: read, erase and add data to the tape.
The third part is a consequence of the previous ones, describing the Turing machine in traditional terms identifying the reading head and the transformation rules.
Cook provides a list of gliders in the evolution space of Rule 110 [6] more complete than the one presented by Lind, leaving open the problem of finding more gliders. As in The Game of Life, it is interesting to know the number of structures that can exist in the evolution space, the list shows each one of the gliders and the extensions that some of them may have. This list has been reproduced through collisions and can be consulted in [15].