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A332087 Diagonals of cellular automata with 4 conditions and 6 possible values.

%I A332087 #23 Oct 05 2020 01:06:48
%S A332087 3,33,333,3333,33433,334433,3344433,33433433,334444433,3344444433,
%T A332087 33434443433,334445544433,3344455544433,33434000043433,
%U A332087 334444444444433,3344444334444433,33434400000443433,334445433334544433,3344454322234544433,33434050022005043433,3344444433333344444433
%N A332087 Diagonals of cellular automata with 4 conditions and 6 possible values.
%C A332087 The automata starts with 2 entries on each axis of value 3.
%C A332087 Defined value(u,v) for any u,v natural the value of each cell of the automata.
%C A332087 The axis(u,0),(u,-1) and (0,v),(-1,v) are value 3.
%C A332087 Matrix (with entries):
%C A332087 33333333333333
%C A332087 33333333333333
%C A332087 33444444444444 ...
%C A332087 33443443443443
%C A332087 33434444444444
%C A332087 33444455044444
%C A332087 33444550440440
%C A332087 33434504303303
%C A332087 33444043032032
%C A332087 33443440322322
%C A332087 ...          ...
%C A332087 Diagonals:
%C A332087 4
%C A332087 44
%C A332087 444
%C A332087 4334
%C A332087 44444
%C A332087 444444
%C A332087 4344434
%C A332087 44455444
%C A332087 444555444
%C A332087 4340000434
%C A332087 44444444444
%C A332087 444443344444
%C A332087 4344000004434
%C A332087 44454333345444
%C A332087 444543222345444
%C A332087 4340500220050434
%C A332087 44444433333444444
%C A332087 ...
%C A332087 The stable parts around the axis are built with the matrix:
%C A332087 33434
%C A332087 30444
%C A332087 44134
%C A332087 34314
%C A332087 44440
%C A332087 until approximately at a(300), when it disappears, and form a more chaotic structure that covers all the area of (u+175,v+175).
%H A332087 Mario Cortés, <a href="/A332087/a332087.pdf">VISUAL REPRESENTATION WITH COLORS</a>
%F A332087 value(v,u)= (In order of priority)
%F A332087 if( (v,u-1)+(v-1,u)+(v-1,u-1)+(v,u-2)+(v-2,u)-(v-1,u-2)-(v-2,u-1) )>10;0
%F A332087 if( (v,u-1)+(v-1,u)+(v-1,u-1)-(v,u-2)-(v-2,u) )=5;3
%F A332087 if( (v,u-1)+(v-1,u)+(v-1,u-1)+(v-1,u-2)+(v-2,u-1)-(v-2,u-2) )=3;2
%F A332087 if( (v-1,u-2)+(v-2,u-1)+(v-2,u-2)+(v-1,u-1)-(v,u-1)-(v-1,u) )=1;1
%F A332087 if nothing= floor(((v,u-1)+(v-1,u)+(v-1,u-1)+(v,u-2)+(v-2,u)-(v-1,u-2)-(v-2,u-1))/7 +1)
%e A332087 value(1,1) = floor(((3)+(3)+(3)+(3)+(3)+(3)+(3))/7 +1) = 4,
%e A332087 value(1,2) = floor(((4)+(3)+(3)+(3)+(3)+(3)+(3))/7 +1) = 4,
%e A332087 value(2,1) = floor(((3)+(4)+(3)+(3)+(3)+(3)+(3))/7 +1) = 4,
%e A332087 ...
%Y A332087 Cf. A006943.
%K A332087 nonn
%O A332087 1,1
%A A332087 _Mario Cortés_, Aug 22 2020