Difference between revisions of "Template"

Revision as of 16:53, 5 August 2023

A template is a minimal pattern that guarantees some kind of connection. There are several different (and sometimes overlapping) types:

• Edge templates
• Ladder escape templates
• Interior templates
• Second order templates

Carrier

The carrier of a template consists of all of those cells (occupied or empty) that are part of the template. Empty cells in a template's carrier are an important part of the template and must not be ignored. If any of these cells are occupied by the opponent, the template is no longer valid.

Validity

We say that a proposed template is valid if it actually guarantees the kind of connection that it is claimed to guarantee, and invalid otherwise.

Minimality

Templates are, by definition, minimal. This means that removing any of the stones or empty hexes from the template would invalidate the template. For example, the following pattern guarantees a virtual connection of the red stones to the edge. However, it is not a template, because it is not minimal.

The following pattern has a smaller carrier and guarantees the same connection. It is minimal, i.e., removing any more empty hexes or any red stone makes the pattern invalid. Since the pattern is both valid and minimal, it is a template. It is known as edge template IV-2-a.

Overlapping templates

Two templates overlap if some empty cell belongs to both of their carriers. Care must be taken with overlapping templates: although each template may be valid individually, the overlapping templates may not form a valid connection as a whole. The simplest example is the following situation, called a U-turn:

Although 1 is connected to 2 via a valid bridge template, and 2 is connected to 3 via a valid bridge template, 1 is not connected to 3, because the bridges overlap at *. In fact, if Blue plays at *, Red cannot defend both bridges in a single move.

See also

• Naming of templates

Reference

• David King's Hex template page