Pattern naming convention

[Neon22]

A problem seems to be that there are many patterns and they are hard to describe. Currently they are identifed by an increasing number but the value has no relationship to the pattern. Maintaining this order will be difficult. A side effect is that its hard to refer to a specific pattern when describing it to someone.

Features of the patterns:

• There is a small number of core tilings (in comparison to patterns) E.g. 2x2, 2x4, 4x4, etc...
• There is a compact form that describes the incoming connections in a compressed 10 symbol alphabet. But this only works for connections of stride 1.
  • I.e. the link is between adjacent dots, no more than one unit away from each other in the tile.
• Other strides are possible but there is no compact form yet. The outgoing uncompressed form can describe these adequately but is not compact.
• To connect two patterns together they need to share boundary dot locations (not sure if this is really true or just a convention). So boundary dot locations could be used to find adjacent patterns to smoothly connect to in more complex patterns.
• For any given tiling and stride (set), there is a finite number of patterns. Once discovered there are no more.
• There may be many redundant descriptions of the same pattern in this set.
  • These duplicates can be identified by shifting the pattern, or by mirroring (for symmetrical patterns).
  • Simpler linear shifting of the compact form, can detect permutations.
  • Mirrors can be detected by looking for a palindrome at one place in the shifting cycle. Mirroring in a 4x4 pattern is equivalent to a 4x2 pattern.

Possible naming convention: One likely possibility is to group patterns by tiling and stride. Then by the first three digits of their compact form. The individual label being their compact form which is unique. E.g. "4x4s1_586--4-55-21-5-7", "4x4s1_4831-4-72828-4--"

• These could then be sorted in numeric order and appear eveyrwhere in the same order.
• Initially when exploring a new NxM tiling and stride, the naming convention would hold but the order would be unknown until it had been explored.
• Tailing - characters can be ignored as they can be reconstructed from the tiling section.

This means:

• These could then be sorted in numeric order and appear eveyrwhere in the same order.
• Someone can refer to a pattern by the three digit prefix and some pattern in the tail.
• E.g. For the pinwheel. This would be "4x4s1_586--4-55-21-5-7"
  • When referring to it anecdotally it becomes a 4x4 pattern starting with 586 and having a 55 in the tail.
  • This simple description resolves to only 4 patterns.
• Patterns starting with - would not exist as they can be shifted until there is a dot in the first position. (this may already be the case).
• The placement of dots is defined by the absence of "-" characters. This may help with finding other patterns to easily connect with.

Additionally: Some patterns are more interesting than others and will have names. A list of common named patterns can be aliased to the identifier. Many of these named patterns will have different names for the same patterns due to the widespread nature of this activity.

[Neon22]

I had another insight. All larger patterns can be described by smaller patterns alongside each other. This becomes more complex as stride of some sub-patterns lengthen. This approach would lower the complexity of the name a great deal.