Surjective：Make sure there is no one left

[Dylan Chen]

In the 3 months contributing to Catagolue, I can't help wondering that what is the final purpose of Soup Search. The enormous computing resources spent on Soup Search seems meaningless comparing SAT-like solver, which is more effective of searching certain patterns.
Yesterday morning, some fresh ideas have came to me. Get me a better understanding of CGOL related concept.

1. Form the view of timeline.
For each given state S, next generation S* is unique and certain. It is easy to calculate next gen(you can do it with pencil and paper by hand).However the reverse process is much more harder, to find the previous generation, the parent(s).Nevertheless, the origin S0 state, which has no parent(s), so called Garden of Eden.

[Dylan Chen]

2. Get the concept "jective"

The img shows several concept explicitly

Surjective
Every B has A or As(No B left)

Injective
Every A has its own unique B(Many to one is not OK)

[Dylan Chen]

In timeline view, all of finite patterns can be organized in order, forming plenty of timelines.

Here are three basic kind of timeline demo

[Dylan Chen]

All 16x16 patterns of APGsearch could be regarded as a huge cluster of timelines (2^256).
Some of them will intersect(merge), some won’t .


The purpose of soup search is:
1.to find the precursor of patterns that we interested in. (how did timelines develop )
2.to find undiscovered timeline. (discover new timeline)

[wzkchem5]

A very inconvenient thing is that each pattern A that has at least one predecessor B has an infinite number of predecessors, i.e. the pattern B plus a few sparks that are sufficiently far away. So the full timeline cannot really be drawn.