Why can Conway’s Game of Life be classified as a universal machine?

青春壹個敷衍的年華 提交于 2019-11-29 19:05:17

You can build a Turing machine out of Conway's life - although it would be pretty horrendous.

The key is in gliders (and related patterns) - these move (slowly) along the playing field, so can represent streams of bits (the presence of a glider for a 1 and the absence for a 0). Other patterns can be built to take in two streams of gliders (at right angles) and emit another stream of bits corresponding to the AND/OR/etc of the original two streams.

EDIT: There's more on this on the LogiCell web site.

Paul Rendell implemented a Turing machine in Life. Gliders represent signals, and interactions between them are gates and logic that together can create larger components which implement the Turing machine.

Basically, any automatic machinery that can implement AND, OR, and NOT can be combined together in complex enough ways to be Turing-complete. It's not a useful way to compute, but it meets the criteria.

Conway's "Life" can be taken even further: It's not only possible to build a Life pattern that implements a Universal Turing Machine, but also a Von Neumann "Universal Constructor:" http://conwaylife.com/wiki/Universal_constructor

Since a "Universal Constructor" can be programmed to construct any pattern of cells, including a copy of itself, Coway's "Life" is therefore capable of "self-replication," not just Universal Computation.

I highly recommend the book The Recursive Universe by Poundstone. Out of print, but you can probably find a copy, perhaps in a good library. It's almost all about the power of Conway's Life, and the things that can exist in a universe with that set of natural laws, including self-reproducing entities and IIRC, Darwinian evolution.

And Paul Chapman actually build a universal turing machine with game of life: http://www.igblan.free-online.co.uk/igblan/ca/ by building a "Universal Minsky Register Machine".

The pattern is constructed on a lattice of 30x30 squares. Lightweight Spaceships (LWSSs) are used to communicate between components, which have P60 logic (except for Registers - see below). A LWSS takes 60 generations to cross a lattice square. Every 60 generations, therefore, any inter-component LWSS (pulse) is in the same position relative to the square it's in, allowing for rotation

.

易学教程内所有资源均来自网络或用户发布的内容,如有违反法律规定的内容欢迎反馈
该文章没有解决你所遇到的问题?点击提问,说说你的问题,让更多的人一起探讨吧!