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A332087
Diagonals of cellular automata with 4 conditions and 6 possible values.
1
3, 33, 333, 3333, 33433, 334433, 3344433, 33433433, 334444433, 3344444433, 33434443433, 334445544433, 3344455544433, 33434000043433, 334444444444433, 3344444334444433, 33434400000443433, 334445433334544433, 3344454322234544433, 33434050022005043433, 3344444433333344444433
OFFSET
1,1
COMMENTS
The automata starts with 2 entries on each axis of value 3.
Defined value(u,v) for any u,v natural the value of each cell of the automata.
The axis(u,0),(u,-1) and (0,v),(-1,v) are value 3.
Matrix (with entries):
33333333333333
33333333333333
33444444444444 ...
33443443443443
33434444444444
33444455044444
33444550440440
33434504303303
33444043032032
33443440322322
... ...
Diagonals:
4
44
444
4334
44444
444444
4344434
44455444
444555444
4340000434
44444444444
444443344444
4344000004434
44454333345444
444543222345444
4340500220050434
44444433333444444
...
The stable parts around the axis are built with the matrix:
33434
30444
44134
34314
44440
until approximately at a(300), when it disappears, and form a more chaotic structure that covers all the area of (u+175,v+175).
FORMULA
value(v,u)= (In order of priority)
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
if( (v,u-1)+(v-1,u)+(v-1,u-1)-(v,u-2)-(v-2,u) )=5;3
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
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
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)
EXAMPLE
value(1,1) = floor(((3)+(3)+(3)+(3)+(3)+(3)+(3))/7 +1) = 4,
value(1,2) = floor(((4)+(3)+(3)+(3)+(3)+(3)+(3))/7 +1) = 4,
value(2,1) = floor(((3)+(4)+(3)+(3)+(3)+(3)+(3))/7 +1) = 4,
...
CROSSREFS
Cf. A006943.
Sequence in context: A362478 A221883 A002277 * A001507 A221162 A231594
KEYWORD
nonn
AUTHOR
Mario Cortés, Aug 22 2020
STATUS
approved