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

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).

Links

Table of n, a(n) for n=1..21.

Mario Cortés, VISUAL REPRESENTATION WITH COLORS

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

Adjacent sequences: A332084 A332085 A332086 * A332088 A332089 A332090

Keyword

nonn

Author

Mario Cortés, Aug 22 2020

Status

approved