One-dimensional cellular automata
You are encouraged to solve this task according to the task description, using any language you may know.
Assume an array of cells with an initial distribution of live and dead cells, and imaginary cells off the end of the array having fixed values.
Cells in the next generation of the array are calculated based on the value of the cell and its left and right nearest neighbours in the current generation. If, in the following table, a live cell is represented by 1 and a dead cell by 0 then to generate the value of the cell at a particular index in the array of cellular values you use the following table:
000 -> 0 # 001 -> 0 # 010 -> 0 # Dies without enough neighbours 011 -> 1 # Needs one neighbour to survive 100 -> 0 # 101 -> 1 # Two neighbours giving birth 110 -> 1 # Needs one neighbour to survive 111 -> 0 # Starved to death.
Ada
<lang ada> with Ada.Text_IO; use Ada.Text_IO;
procedure Cellular_Automata is
type Petri_Dish is array (Positive range <>) of Boolean;
procedure Step (Culture : in out Petri_Dish) is Left : Boolean := False; This : Boolean; Right : Boolean; begin for Index in Culture'First..Culture'Last - 1 loop Right := Culture (Index + 1); This := Culture (Index); Culture (Index) := (This and (Left xor Right)) or (not This and Left and Right); Left := This; end loop; Culture (Culture'Last) := Culture (Culture'Last) and not Left; end Step; procedure Put (Culture : Petri_Dish) is begin for Index in Culture'Range loop if Culture (Index) then Put ('#'); else Put ('_'); end if; end loop; end Put;
Culture : Petri_Dish := ( False, True, True, True, False, True, True, False, True, False, True, False, True, False, True, False, False, True, False, False );
begin
for Generation in 0..9 loop Put ("Generation" & Integer'Image (Generation) & ' '); Put (Culture); New_Line; Step (Culture); end loop;
end Cellular_Automata; </lang> The implementation defines Petri dish type with Boolean items identifying whether a place is occupied by a living cell. State transition is determined by a simple Boolean expression of three arguments. Sample output:
Generation 0 _###_##_#_#_#_#__#__ Generation 1 _#_#####_#_#_#______ Generation 2 __##___##_#_#_______ Generation 3 __##___###_#________ Generation 4 __##___#_##_________ Generation 5 __##____###_________ Generation 6 __##____#_#_________ Generation 7 __##_____#__________ Generation 8 __##________________ Generation 9 __##________________
ALGOL 68
Using the low level packed arrays of BITS manipulation operators
INT stop generation = 9; INT universe width = 20; FORMAT alive or dead = $b("#","_")$; BITS universe := 2r01110110101010100100; # universe := BIN ( ENTIER ( random * max int ) ); # INT upb universe = bits width; INT lwb universe = bits width - universe width + 1; PROC couple = (BITS parent, INT lwb, upb)BOOL: ( SHORT INT sum := 0; FOR bit FROM lwb TO upb DO sum +:= ABS (bit ELEM parent) OD; sum = 2 ); FOR generation FROM 0 WHILE printf(($"Generation "d": "$, generation, $f(alive or dead)$, []BOOL(universe)[lwb universe:upb universe], $l$)); # WHILE # generation < stop generation DO BITS next universe := 2r0; # process the first event horizon manually # IF couple(universe,lwb universe,lwb universe + 1) THEN next universe := 2r10 FI; # process the middle kingdom in a loop # FOR bit FROM lwb universe + 1 TO upb universe - 1 DO IF couple(universe,bit-1,bit+1) THEN next universe := next universe OR 2r1 FI; next universe := next universe SHL 1 OD; # process the last event horizon manually # IF couple(universe, upb universe - 1, upb universe) THEN next universe := next universe OR 2r1 FI; universe := next universe OD
Using high level BOOL arrays
INT stop generation = 9; INT upb universe = 20; FORMAT alive or dead = $b("#","_")$; BITS bits universe := 2r01110110101010100100; # bits universe := BIN ( ENTIER ( random * max int ) ); # [upb universe] BOOL universe := []BOOL(bits universe)[bits width - upb universe + 1:]; PROC couple = (REF[]BOOL parent)BOOL: ( SHORT INT sum := 0; FOR bit FROM LWB parent TO UPB parent DO sum +:= ABS (parent[bit]) OD; sum = 2 ); FOR generation FROM 0 WHILE printf(($"Generation "d": "$, generation, $f(alive or dead)$, universe, $l$)); # WHILE # generation < stop generation DO [UPB universe]BOOL next universe; # process the first event horizon manually # next universe[1] := couple(universe[:2]); # process the middle kingdom in a loop # FOR bit FROM LWB universe + 1 TO UPB universe - 1 DO next universe[bit] := couple(universe[bit-1:bit+1]) OD; # process the last event horizon manually # next universe[UPB universe] := couple(universe[UPB universe - 1: ]); universe := next universe OD
Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
BASIC
<lang qbasic>DECLARE FUNCTION life$ (lastGen$) DECLARE FUNCTION getNeighbors! (group$) CLS start$ = "_###_##_#_#_#_#__#__" numGens = 10 FOR i = 0 TO numGens - 1 PRINT "Generation"; i; ": "; start$ start$ = life$(start$) NEXT i
FUNCTION getNeighbors (group$) ans = 0 IF (MID$(group$, 1, 1) = "#") THEN ans = ans + 1 IF (MID$(group$, 3, 1) = "#") THEN ans = ans + 1 getNeighbors = ans END FUNCTION
FUNCTION life$ (lastGen$) newGen$ = "" FOR i = 1 TO LEN(lastGen$) neighbors = 0 IF (i = 1) THEN 'left edge IF MID$(lastGen$, 2, 1) = "#" THEN neighbors = 1 ELSE neighbors = 0 END IF ELSEIF (i = LEN(lastGen$)) THEN 'right edge IF MID$(lastGen$, LEN(lastGen$) - 1, 1) = "#" THEN neighbors = 1 ELSE neighbors = 0 END IF ELSE 'middle neighbors = getNeighbors(MID$(lastGen$, i - 1, 3)) END IF
IF (neighbors = 0) THEN 'dies or stays dead with no neighbors newGen$ = newGen$ + "_" END IF IF (neighbors = 1) THEN 'stays with one neighbor newGen$ = newGen$ + MID$(lastGen$, i, 1) END IF IF (neighbors = 2) THEN 'flips with two neighbors IF MID$(lastGen$, i, 1) = "#" THEN newGen$ = newGen$ + "_" ELSE newGen$ = newGen$ + "#" END IF END IF NEXT i life$ = newGen$ END FUNCTION</lang> Output:
Generation 0 : _###_##_#_#_#_#__#__ Generation 1 : _#_#####_#_#_#______ Generation 2 : __##___##_#_#_______ Generation 3 : __##___###_#________ Generation 4 : __##___#_##_________ Generation 5 : __##____###_________ Generation 6 : __##____#_#_________ Generation 7 : __##_____#__________ Generation 8 : __##________________ Generation 9 : __##________________
C
<lang c>#include <stdio.h>
- include <stdlib.h>
- include <string.h>
- define SPACEDIM 20
- define GENERATION 10
- define ALIVE '#'
- define DEAD '_'
/* what happens out of the space: is the world a circle, or
it really ends? */
- define CCOND 0
char space[SPACEDIM]; char tspace[SPACEDIM];
int rrand(int l) {
return (int)((double)l*(double)rand()/((double)RAND_MAX+1.0));
}
void initspace(char *s, int d) {
int i; char *tp = "_###_##_#_#_#_#__#__"; for(i=0; (i < strlen(tp)) && (i<d) ; i++) { s[i] = (tp[i] == ALIVE) ? 1 : 0; }
}
void initspace_random(char *s, int d) {
int i; for (i=0; i<d; i++) { s[i] = rrand(2); }
}
/*
count the Number of Alive in the Neighbourhood two kind of "bound condition" can be choosen at compile time
- /
int nalive(char *s, int i, int d) {
switch ( CCOND ) { case 0: return ((i-1)<0 ? 0 : s[i-1]) + ((i+1)<d ? s[i+1] : 0 ); case 1: return s[ (i+1)%d ] + s[ (i+d-1)%d ]; }
}
void evolve(char *from, char *to, int d) {
int i; for(i=0; i<d; i++) { if ( from[i] ) { /* 0 neighbour is solitude, 2 are one too much; 1, he's a friend */ if ( nalive(from, i, d) == 1 ) { to[i] = 1; } else { to[i] = 0; } } else { if ( nalive(from, i, d) == 2 ) { /* there must be two, to make a child ... */ to[i] = 1; } else { to[i] = 0; } } }
}
void show(char *s, int d) {
int i; for(i=0; i<d; i++) { printf("%c", s[i] ? ALIVE : DEAD); } printf("\n");
}
int main()
{
int i; char *from, *to, *t; initspace(space, SPACEDIM); from = space; to = tspace; for(i=0; i<GENERATION; i++) { show(from, SPACEDIM); evolve(from, to, SPACEDIM); t = from; from = to; to = t; } printf("\n"); initspace_random(space, SPACEDIM); from = space; to = tspace; for(i=0; i<GENERATION; i++) { show(from, SPACEDIM); evolve(from, to, SPACEDIM); t = from; from = to; to = t; } return 0;
} </lang>
The output is:
_###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________ __##________________ #_###__#_#_#_#####_# _##_#___#_#_##___##_ _###_____#_###___##_ _#_#______##_#___##_ __#_______###____##_ __________#_#____##_ ___________#_____##_ _________________##_ _________________##_ _________________##_
Forth
: init ( bits count -- ) 0 do dup 1 and c, 2/ loop drop ; 20 constant size create state $2556e size init 0 c, : .state cr size 0 do state i + c@ if ." #" else space then loop ; : ctable create does> + c@ ; ctable rules $68 8 init : gen state c@ ( window ) size 0 do 2* state i + 1+ c@ or 7 and dup rules state i + c! loop drop ; : life1d ( n -- ) .state 1 do gen .state loop ;
10 life1d
Fortran
<lang fortran> PROGRAM LIFE_1D
IMPLICIT NONE LOGICAL :: cells(20) = (/ .FALSE., .TRUE., .TRUE., .TRUE., .FALSE., .TRUE., .TRUE., .FALSE., .TRUE., .FALSE., & .TRUE., .FALSE., .TRUE., .FALSE., .TRUE., .FALSE., .FALSE., .TRUE., .FALSE., .FALSE. /) INTEGER :: i DO i = 0, 9 WRITE(*, "(A,I0,A)", ADVANCE = "NO") "Generation ", i, ": " CALL Drawgen(cells) CALL Nextgen(cells) END DO CONTAINS SUBROUTINE Nextgen(cells) LOGICAL, INTENT (IN OUT) :: cells(:) LOGICAL :: left, centre, right INTEGER :: i left = .FALSE. DO i = 1, SIZE(cells)-1 centre = cells(i) right = cells(i+1) IF (left .AND. right) THEN cells(i) = .NOT. cells(i) ELSE IF (.NOT. left .AND. .NOT. right) THEN cells(i) = .FALSE. END IF left = centre END DO cells(SIZE(cells)) = left .AND. right END SUBROUTINE Nextgen SUBROUTINE Drawgen(cells) LOGICAL, INTENT (IN OUT) :: cells(:) INTEGER :: i DO i = 1, SIZE(cells) IF (cells(i)) THEN WRITE(*, "(A)", ADVANCE = "NO") "#" ELSE WRITE(*, "(A)", ADVANCE = "NO") "_" END IF END DO WRITE(*,*) END SUBROUTINE Drawgen END PROGRAM LIFE_1D</lang>
Output
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Haskell
module Life1D where import Data.List import System.Random import Control.Monad import Control.Arrow bnd :: [Char] -> Char bnd bs = case bs of "_##" -> '#' "#_#" -> '#' "##_" -> '#' _ -> '_' donxt xs = unfoldr(\xs -> case xs of [_,_] -> Nothing ; _ -> Just (bnd $ take 3 xs, drop 1 xs)) $ '_':xs++"_" lahmahgaan xs = init.until (liftM2 (==) last (last. init)) (ap (++)(return. donxt. last)) $ [xs, donxt xs] main = do g <- newStdGen let oersoep = map ("_#"!!). take 36 $ randomRs(0,1) g mapM_ print . lahmahgaan $ oersoep
Some output:
*Life1D> mapM_ print . lahmahgaan $ "_###_##_#_#_#_#__#__" "_###_##_#_#_#_#__#__" "_#_#####_#_#_#______" "__##___##_#_#_______" "__##___###_#________" "__##___#_##_________" "__##____###_________" "__##____#_#_________" "__##_____#__________" "__##________________" *Life1D> main "__##_##__#____###__#__#_______#_#_##" "__#####_______#_#______________#_###" "__#___#________#________________##_#" "________________________________###_" "________________________________#_#_" "_________________________________#__" "____________________________________"
J
life1d=: '_#'{~]@(([:3&(2=+/\)0,],0:)^:a:)
Example use:
life1d ? 20 # 2 _###_##_#_#_#_#__#__ _#_#####_#_#_#______ __##___##_#_#_______ __##___###_#________ __##___#_##_________ __##____###_________ __##____#_#_________ __##_____#__________ __##________________
Java
This example requires a starting generation of at least length two (which is what you need for anything interesting anyway). <lang java>public class Life{ public static void main(String[] args) throws Exception{ String start= "_###_##_#_#_#_#__#__"; int numGens = 10; for(int i= 0; i < numGens; i++){ System.out.println("Generation " + i + ": " + start); start= life(start); } }
public static String life(String lastGen){ String newGen= ""; for(int i= 0; i < lastGen.length(); i++){ int neighbors= 0; if (i == 0){//left edge neighbors= lastGen.charAt(1) == '#' ? 1 : 0; } else if (i == lastGen.length() - 1){//right edge neighbors= lastGen.charAt(i - 1) == '#' ? 1 : 0; } else{//middle neighbors= getNeighbors(lastGen.substring(i - 1, i + 2)); }
if (neighbors == 0){//dies or stays dead with no neighbors newGen+= "_"; } if (neighbors == 1){//stays with one neighbor newGen+= lastGen.charAt(i); } if (neighbors == 2){//flips with two neighbors newGen+= lastGen.charAt(i) == '#' ? "_" : "#"; } } return newGen; }
public static int getNeighbors(String group){ int ans= 0; if (group.charAt(0) == '#') ans++; if (group.charAt(2) == '#') ans++; return ans; } }</lang> Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
Modula-3
Modula-3 provides a module Word
for doing bitwise operations, but it segfaults when trying to use BOOLEAN
types, so we use INTEGER
instead.
<lang modula3>MODULE Cell EXPORTS Main;
IMPORT IO, Fmt, Word;
VAR culture := ARRAY [0..19] OF INTEGER {0, 1, 1, 1,
0, 1, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 0, 1, 0, 0};
PROCEDURE Step(VAR culture: ARRAY OF INTEGER) =
VAR left: INTEGER := 0; this, right: INTEGER; BEGIN FOR i := FIRST(culture) TO LAST(culture) - 1 DO right := culture[i + 1]; this := culture[i]; culture[i] := Word.Or(Word.And(this, Word.Xor(left, right)), Word.And(Word.Not(this), Word.And(left, right))); left := this; END; culture[LAST(culture)] := Word.And(culture[LAST(culture)], Word.Not(left)); END Step;
PROCEDURE Put(VAR culture: ARRAY OF INTEGER) =
BEGIN FOR i := FIRST(culture) TO LAST(culture) DO IF culture[i] = 1 THEN IO.PutChar('#'); ELSE IO.PutChar('_'); END; END; END Put;
BEGIN
FOR i := 0 TO 9 DO IO.Put("Generation " & Fmt.Int(i) & " "); Put(culture); IO.Put("\n"); Step(culture); END;
END Cell.</lang> Output:
Generation 0 _###_##_#_#_#_#__#__ Generation 1 _#_#####_#_#_#______ Generation 2 __##___##_#_#_______ Generation 3 __##___###_#________ Generation 4 __##___#_##_________ Generation 5 __##____###_________ Generation 6 __##____#_#_________ Generation 7 __##_____#__________ Generation 8 __##________________ Generation 9 __##________________
Nial
(life.nial)
% we need a way to write a values and pass the same back wi is rest link [write, pass] % calculate the neighbors by rotating the array left and right and joining them neighbors is pack [pass, sum [-1 rotate, 1 rotate]] % calculate the individual birth and death of a single array element igen is fork [ = [ + [first, second], 3 first], 0 first, = [ + [first, second], 2 first], 1 first, 0 first ] % apply that to the array nextgen is each igen neighbors % 42 life is fork [ > [sum pass, 0 first], life nextgen wi, pass ]
Using it
|loaddefs 'life.nial' |I := [0,1,1,1,0,1,1,0,1,0,1,0,1,0,1,0,0,1,0,0] |life I
OCaml
<lang ocaml>let get g i =
try g.(i) with _ -> 0
let next_cell g i =
match get g (i-1), get g (i), get g (i+1) with | 0, 0, 0 -> 0 | 0, 0, 1 -> 0 | 0, 1, 0 -> 0 | 0, 1, 1 -> 1 | 1, 0, 0 -> 0 | 1, 0, 1 -> 1 | 1, 1, 0 -> 1 | 1, 1, 1 -> 0 | _ -> assert(false)
let next g =
let old_g = Array.copy g in for i = 0 to pred(Array.length g) do g.(i) <- (next_cell old_g i) done
let print_g g =
for i = 0 to pred(Array.length g) do if g.(i) = 0 then print_char '_' else print_char '#' done; print_newline()
</lang>
put the code above in a file named "life.ml", and then use it in the ocaml toplevel like this:
#use "life.ml" ;; let iter n g = for i = 0 to n do Printf.printf "Generation %d: " i; print_g g; next g; done ;; let g_of_string str = let f = (function '_' -> 0 | '#' -> 1 | _ -> assert false) in Array.init (String.length str) (fun i -> f str.[i]) ;; # iter 9 (g_of_string "_###_##_#_#_#_#__#__") ;; Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________ - : unit = ()
Python
<lang python>import random
printdead, printlive = '_#' maxgenerations = 10 cellcount = 20 offendvalue = '0'
universe = .join(random.choice('01') for i in range(cellcount))
neighbours2newstate = {
'000': '0', '001': '0', '010': '0', '011': '1', '100': '0', '101': '1', '110': '1', '111': '0', }
for i in range(maxgenerations):
print "Generation %3i: %s" % ( i, universe.replace('0', printdead).replace('1', printlive) ) universe = offendvalue + universe + offendvalue universe = .join(neighbours2newstate[universe[i:i+3]] for i in range(cellcount))
</lang> Sample output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________
The following implementation uses boolean operations to realize the function.
<lang python>import random
nquads = 5 maxgenerations = 10 fmt = '%%0%ix'%nquads nbits = 4*nquads a = random.getrandbits(nbits) << 1
- a = int('01110110101010100100', 2) << 1
endmask = (2<<nbits)-2; endvals = 0<<(nbits+1) | 0 tr = ('____', '___#', '__#_', '__##', '_#__', '_#_#', '_##_', '_###',
'#___', '#__#', '#_#_', '#_##', '##__', '##_#', '###_', '####' )
for i in range(maxgenerations):
print "Generation %3i: %s" % (i,(.join(tr[int(t,16)] for t in (fmt%(a>>1))))) a |= endvals a = ((a&((a<<1) | (a>>1))) ^ ((a<<1)&(a>>1))) & endmask</lang>
Tcl
<lang tcl>proc evolve {a} {
set new [list] for {set i 0} {$i < [llength $a]} {incr i} { lappend new [fate $a $i] } return $new
}
proc fate {a i} {
return [expr {[sum $a $i] == 2}]
}
proc sum {a i} {
set sum 0 set start [expr {$i - 1 < 0 ? 0 : $i - 1}] set end [expr {$i + 1 >= [llength $a] ? $i : $i + 1}] for {set j $start} {$j <= $end} {incr j} { incr sum [lindex $a $j] } return $sum
}
proc print {a} {
puts [string map {0 _ 1 #} [join $a ""]]
}
proc parse {s} {
return [split [string map {_ 0 # 1} $s] ""]
}
set array [parse "_###_##_#_#_#_#__#__"] print $array while {[set new [evolve $array]] ne $array} {
set array $new print $array
}</lang>
Vedit macro language
This implementation writes the calculated patterns into an edit buffer, where the results can viewed and saved into a file if required. The edit buffer also acts as storage during calculations.
IT("Gen 0: ..###.##.#.#.#.#..#.....") // initial pattern #9 = Cur_Col for (#8 = 1; #8 < 10; #8++) { // 10 generations Goto_Col(7) Reg_Empty(20) while (Cur_Col < #9-1) { if (Match("|{##|!#,#.#,|!###}")==0) { Reg_Set(20, "#", APPEND) } else { Reg_Set(20, ".", APPEND) } Char } EOL IN IT("Gen ") Num_Ins(#8, LEFT+NOCR) IT(": ") Reg_Ins(20) }
Sample output:
Gen 0: ..###.##.#.#.#.#..#..... Gen 1: ..#.#####.#.#.#......... Gen 2: ...##...##.#.#.......... Gen 3: ...##...###.#........... Gen 4: ...##...#.##............ Gen 5: ...##....###............ Gen 6: ...##....#.#............ Gen 7: ...##.....#............. Gen 8: ...##................... Gen 9: ...##...................
Logo
works with UCBLogo <lang Logo> make "cell_list [0 1 1 1 0 1 1 0 1 0 1 0 1 0 1 0 0 1 0 0] make "generations 9
to evolve :n ifelse :n=1 [make "nminus1 item :cell_count :cell_list][make "nminus1 item :n-1 :cell_list] ifelse :n=:cell_count[make "nplus1 item 1 :cell_list][make "nplus1 item :n+1 :cell_list] ifelse ((item :n :cell_list)=0) [ ifelse (and (:nminus1=1) (:nplus1=1)) [output 1][output (item :n :cell_list)] ][ ifelse (and (:nminus1=1) (:nplus1=1)) [output 0][ ifelse and (:nminus1=0) (:nplus1=0) [output 0][output (item :n :cell_list)]] ] end
to CA_1D :cell_list :generations make "cell_count count :cell_list (print ") make "printout " repeat :cell_count [ make "printout word :printout ifelse (item repcount :cell_list)=1 ["#]["_] ] (print "Generation "0: :printout)
repeat :generations [
(make "cell_list_temp []) repeat :cell_count[ (make "cell_list_temp (lput (evolve repcount) :cell_list_temp)) ] make "cell_list :cell_list_temp make "printout " repeat :cell_count [ make "printout word :printout ifelse (item repcount :cell_list)=1 ["#]["_] ] (print "Generation word repcount ": :printout)
] end
CA_1D :cell_list :generations </lang> Sample Output:
Generation 0: _###_##_#_#_#_#__#__ Generation 1: _#_#####_#_#_#______ Generation 2: __##___##_#_#_______ Generation 3: __##___###_#________ Generation 4: __##___#_##_________ Generation 5: __##____###_________ Generation 6: __##____#_#_________ Generation 7: __##_____#__________ Generation 8: __##________________ Generation 9: __##________________