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2020-07-14 22:03 Arno  
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as an illustration, This cave shows the full map when extended to 73 columns, such that each column uses the same Seed2 values on each row. The filling rules of BD1 Cave A are again used.  
  
Here are some pictures showing the underlying numbers:  
  
Seed2:  
<a href="http://www.boulderdash.nl/forum/forumpics/73cycle_seed2.png" target="external">http://www.boulderdash.nl/forum/forumpics/73cycle_seed2.png</a>  
  
Seed1:  
<a href="http://www.boulderdash.nl/forum/forumpics/73cycle_seed1.png" target="external">http://www.boulderdash.nl/forum/forumpics/73cycle_seed1.png</a>  
  
Increment of Seed1:  
<a href="http://www.boulderdash.nl/forum/forumpics/73cycle_seed1_increment.png" target="external">http://www.boulderdash.nl/forum/forumpics/73cycle_seed1_increment.png</a>  
  
While Seed2 repeats each row, Seed1 starts repeating itself from row 14 column 3. That is, after 952 draws.  
  
And  dustin : you noticed earlier that the cave is 'silent' which means there is never empty space directly below | or \.  
This can be easily explained by the formula of Seed1:  
  
S_1 := (S_1 + 128[S_1 odd] + floor(S_2 / 2) + C_2 + C_3) mod 256  
  
For each given position, the item below that position is determined by exactly 73 draws.   
Since S_2 contains a cycle of 73, over 73 draws the terms floor(S_2 / 2) add up to a constant value. I calculated it: it's 213.  
The term 128[S_1 odd], over 73 draws, gives a multiple of 128, which modulo 256 is either 0 or 128.  
If we ignore C_2 and C_3 for a while, this implies that when at some position the number is in [0,49] (that is, | or \),   
after 73 draws the number is in [213,6] (mod 256) or [128,177].  
C_2 and C_3 will still increase the number a bit (on average by about 12), but a value in [50,59] won't be reached, which implies no empty space occurs below | or \. :-D

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2020-07-14 22:12 DarkStoorM  
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That was a really great research,  Arno ! BD is so simple, yet it has so much content to talk about!

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2020-07-14 22:46 dustin  
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a very nice and clear explanation of the silent cave!

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2020-07-15 07:37 Arno  
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thx! I've one more research question related to the rng topic... something for tonight! :-D

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2020-07-15 15:54 dustin  
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the horizontal vs. vertical stack issue? ;d

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2020-07-15 20:09 Arno  
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yess exactly!   
i already have the answer; just need to write a small report for the forum! ;-D

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2020-07-16 22:19 dustin  
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great article again! ;d

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2020-07-17 11:54 Arno  
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thx! ;-)