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© Copyright 1993 Mario Hilgemeier

Pseudocode 3:
     Conversion of the GZR into a "time-series"

      Conversion of an iterate of the GZR into a time-series-like 
fractal graph. The abundances of ciphers in large iterates of the 
GZR are known to be about 49.5101% "1", 32.0352% "2" and 18.4547% 
"3". In the following piece of code, ciphers are interpreted as  "1" 
= up, "2" = down, "3" horizontal (no change). The amounts of 
increase or decrease are adjusted to give an approximately 
horizontal line - at least to get an end value of the time-series 
near the start value (0.0).

Read the next cipher from an iterate of the GZR
if the cipher is
{
   1:value = value    +    0.320352 / (0.320352 + 0.495101); /* up */
   2: value = value   -    0.495101 / (0.320352 + 0.495101); /* down */
   3: /* 0.184547 do nothing */
} 

Note: the cipher abundances of the GZR yield ( 0.495101 * 0.320352) 
/ (0.184547 * 0.184547) = 4.65701, only 0.26 % smaller than 
Feigenbaum's constant (about 4.66920) [11]. Can you explain this, or 
is it just chance?


References   content page


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