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After exploring the ground patterns (here and here), I was scrolling through colored patterns when it jumped out that the same blocks are always called in the same order in the first row. Consider patterns generated from a single seed by three-cell block rules. The blocks invoked on the first row of the pattern are the same for all 256 rules. This is not to say that the active/passive patterns are the same - because obviously they're not. Instead, it says the same blocks are called upon to determine which cells in the first row are to be active or passive.

           
0 0 1 2 4 0 0
           

 

A look at the mechanics indicates:

  • The cell under the seed invokes Block 2; the neighborhood is passive, active, and passive (010)
  • The cell to its left invokes Block 1; the neighborhood is passive, passive, and active (001)
  • The cell to its right invokes Block 4; the neighborhood is active, passive, and passive (100)
  • The rest of the cells in the first row are determined by Block 0 (000)
  • The remaining blocks can not be used because they require at least two active neighboring cells; therefore it is impossible for them to be invoked by a single seed cell in Row 1
  • Once past the first row, the mix of active and passive cells generates the variety of patterns

There are the sixteen possible active / passive patterns generated in the first row where there's a single seed. Blocks 1, 2, and 4 generate eight possible active / passive ground patterns (which are just like the patterns of the eight blocks). Block 0 affects the field cells in the first row. When Rule 0 is set to passive, the resulting field is white / passive. When set to active, the field in the first row is black / active. And from the study of ground patterns, if Block 7 is passive, the field will be striped; if active, the field will be all active.

The Row 1 pattern is used to number the groups so, starting two cells to the left of the seed column, Row 1:

  • 0000 becomes Group 00
  • 0001 becomes Group 01
  • 1000 becomes Group 08
  • 1001 becomes Group 09
  • and so on

The figure below shows the sixteen possible Row 1 patterns for a single seed, three-cell block automaton:

Group       S         Group       S      
00     1 2 4       08     1 2 4    
      S               S      
01     1 2 4       09     1 2 4    
      S               S      
02     1 2 4       10     1 2 4    
      S               S      
03     1 2 4       11     1 2 4    
      S               S      
04     1 2 4       12     1 2 4    
      S               S      
05     1 2 4       13     1 2 4    
      S               S      
06     1 2 4       14     1 2 4    
      S               S      
07     1 2 4       15     1 2 4    

 

Using rule groups become a much more fruitful method to analyze patterns and the mechanics of patterns. Theses links show the grouped patterns, both active passive and color:

As can be seen through the links, using the Rule Groups makes it easier to assess the consistency of patterns. The Field Passive 0 groups (00 through 07) collect like patterns together, with Groups 03 and 06 mirroring each other. Only in Group 07 are there patterns which are unique.

The patterns in the Field Active 0 groups (08 through 15) are more diverse in the types of patterns. Most of the patterns in Group 08 are either the same pattern or mirrors. Groups 09 and 12 and Groups 11 and 14 are mirrors of each other. Groups 10 and 13 appear to have a number of unique patterns while the collection of patterns in Group 15 mimics the consistency of the Field Passive 0 groups.

Rule Groups also makes it easier to track changes in patterns when different seed conditions are applied. Here are links showing the grouped patterns using an m1 seed:

What is striking is while the patterns do change, there is an overall consistency within each rule group.