Chapter 8 – Conclusions

Publisher Summary This chapter explains that there exists a strongly rotation-symmetric 8-state, 5-neighbor cellular space which is computation-construction-universal. In this space all two-dimensional completely passive configurations can be read and erased by other configurations. As a consequence, this space may well be strictly more powerful than von Neumann's rotation-symmetric 29-state, 5-neighbor cellular space. A necessary condition for computation universality is that, by choice of initial configuration, it is possible to obtain boundable propagation arbitrarily far from its source. There does not exist a computation-universal 2-state, 5-neighbor cellular space with a neighborhood that is 90°-rotation-symmetric. However, there does exist a 2-state cellular space that is computation-construction-universal.