pyramidal-reduction

Hypothesis

Can we transform a text by building rewriting rules for it on-the-fly?

Apparatus

• Python 2.7.6 (probably works with older versions too)
• An input sentence

Method

• For each pair of symbols in the input sentence, use a rule to reduce them to a single symbol. This results in a sentence which is one symbol shorter than the previous sentence. Repeat until you have a sentence which is only one symbol long.

• Concerning the rules:

  • if both symbols are a space, use a random symbol from the alphabet.
  • otherwise, and if the right-hand symbol is a space, use a space.
  • otherwise, if there is an already-established rule for this pair of symbols, use it.
  • otherwise, make up a random rule
  • in all cases, record this new rule for future use.

• After you have this one-symbol long sentence, make an inverse mapping of the rules and, using those rules, iteratively expand it to new sentences until you get a sentence which is the same length as the original sentence. (How exactly this happens is probably more easily divined from the code than explained in words.)

Observations

The process is very cellular-automaton-y. If you play with the exact rules regarding space (if either is a space generate a space; don't store space-involving rules; etc.) you can get some very gasket-like patterns happening.

A sample run on the input sentence "It was a dark and stormy night" might result in the following.

I t   w a s   a   d a r k   a n d   s t o r m y   n i g h t . 
 a   a w h   d   t d a     d k w   h w   y   d   m s n n   i 
    d g I   t   . t d   g t a n   o n   k   t   r d g g   a 
   t t a   .   a r t   t i n k   s h   y   .   r s t s   d 
    I n   a   d a .   . d s o   h i   k   a   r r w d   t 
     r   d   t d r   a m   h   o I   y   d   r g   g   . 
        t   . t g   d t   o   s a   k   t   r a   t   a 
       .   a r g   t s   s   h     y   .   r w   .   d 
          d a a   . d   h   o   g k   a   r     a   t 
         t d h   a m   o   s   t     d   r   g d   . 
          t w   d t   s   h   .   g t   r   t s   a 
           y   t s   h   o   a   t i   r   . d   d 
              . d   o   s   d   . d   r   a m   t 
             a m   s   h   t   a m   r   d t   . 
              t   h   o   .   d t   r   t s   a 
                 o   s   a   t s   r   . d   d 
                s   h   d   . d   r   a m   t 
                   o   t   a m   r   d t   . 
                  s   .   d t   r   t s   a 
                     a   t s   r   . d   d 
                    d   . d   r   a m   t 
                       a m   r   d t   . 
                      d t   r   t s   a 
                       s   r   . d   d 
                          r   a m   t 
                         r   d t   . 
                            t s   a 
                           . d   d 
                            m   t 
                               . 
                              a 
                               i 
                            r w g 
                             m a w 
                          I   n   i 
                         h i   d s h 
                        a a i   a a a 
                       a r g t o I t m 
                        w r r . k h m r 
                     k   i r s r m i w r 
                      y   h s I n d   i r 
                   I   k   s I o y w   h s 
                  k h   y   o a i a m   s I 
                 r m i   k   h t . i w   o a 
                r s w g k w   s r t . t o n   
               r s I r r m a   o . r t d w r   
              h s I o . t   .   h a . r a m g k 
             a a a . k h m   t o n   t h t     y 
            d k s m k w n d s r . k   g a m   . i 
           t i g g n g g h r d t w k     . d s r s 
          . r s n n n n n h s t d h w   . a . k g d 
         s r s I . k w r n h m t s o o   t m k w d a 
        . k g g r t w a . k s w . k h g k i w k a . i 
       . a n n n   g g I a n i I a n h r m d h w   t . 
      r t m m m m       w   d   w   d s k n a s t o r t 
     n   d i w m r k   . t o n   i   a a n n   o r . t d 
    r n   a i I r s d   t d w r k I   . i g h t I n r . m 
   . t a   w g r s I g   g k a . h i   t . g a m I . t w m 
    t d k   i n   o a w     y g g a i   g g m   n w g a m r 
 r w . m a   h w   h t h   . i n n   h t g m r   d h r g n   
n   i g n   . y a   s r h   t . k w   s r r y w   a a . g h t

I'm not entirely sure if the occurrences of stor and ght in the expanding pyramid are a result of there being rules that reduce those sequences being run in reverse, or if they are just coincidences.

The mapping used to reduce the original sentence is deterministic (once it has been randomly constructed) — each pair maps to exactly one single symbol. But the inverse mapping is definitely non-deterministic, because each single symbol may map to multiple pairs. So there is "more randomness" in the expanding pyramid than in the shrinking one.