For each (finite) sequence

**X**of patterns (of active cells) there is the set

**OSCILLATOR(X)**of universes in which

**X**is an oscillator (of period |

**X**|).

For each universe

**A**there are minimal sets

**D**of sequences

**X**such that

**A**is in

**SL(X)**and no other universe

**B**is in

**SL(X)**for all

**X**in

**D**.

Such a set

**D**

*defines*the universe

**A**.

It's interesting to find for each universe

**A**a smallest set

**D**of sequences that defines it, "smallest" with respect to

a) the number of sequences

b) the (overall) length of the sequences

c) the (overall) number of active cells involved.

My bunch of questions include:

- What is the smallest set that defines Conway's Game of Life, i.e. B3/S2,3?
- Where do I find a discussion of this topic which I'd like to call "reverse rule-finding" (reflecting terms like reverse engineering or reverse mathematics)?
- Did Conway mention how he found his specific rule (= universe)? Driven by what? (Maybe by some small set of still-lifes and oscillators?)
- What would/could be gained when going further, e.g. from oscillators to spaceships (=
*moving*oscillators)?