Pea pattern

A pea pattern is a mathematical pattern that, when following certain steps, will yield a string of patterned numbers.

The first Pea pattern made goes as such:

A number is first named, such as 1, and the next number is derived by how many of each digit is named in the number. There is one digit in 1, and there are 1 of that number, so the next number is 11. There are two 1's in 11, thus the next number in the series is 21. There is 1 2 and 1 1 in 21, so the number after that is 1211. The original version of the Pea pattern had the digits listed in 'first-up' sequence thus the series for Pea(1) was as follows

1  
11      
21      
1211    
3112    
132112  
311322  
232122  
421311          
14123113                
41141223                
24312213                
32142321
23322114
32232114        these last two form a loop.

This is not the Look-and-Say series which proceeds 1, 11, 21, 1211, 111221.

As originally written the Pea pattern displays how many of each digit occurs in the series. There is an alternative Pea pattern which has the digits in ascending order. Pea(1)A [digits in ascending order] should be 1, 11, 21, 1112, 3112, 211213, 312213, 212223, 114213 etc and it becomes more interesting because Pea(0), Pea(1), Pea(2) & Pea(3) all loop after the 13th or 14th step.

As with the Look-and-say series, beginning with 22 yields an immediate loop. However Pea(33)A proceeds 333, 33, 23, 1213, 211213, etc

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The second pea pattern is somewhat unique in that it goes backwards, beginning with a large number and going back down to a one-digit number. One could begin with a number such as 54739120829. The adjacent numbers are subtracted from one another using absolute value, as such:

54739120829
 1346812867
  212271621
   11056541
    0151113
     144002
      30402
       3442
        102
         12
          1

Using this method the numbers will usually retract to 1 or 0.