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Ulam spiral (for primes): Difference between revisions

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Ulam spiral (for primes) (view source)

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=={{header|ALGOL 68}}==
{{works with|ALGOL 68G|Any - tested with release 2.8.3.win32}}
<syntaxhighlight lang="algol68">
BEGIN # construct a Ulam spiral for primes #
PR read "primes.incl.a68" PR # include prime utilities #
# prints a Ulam spiral for primes with the specified width, #
# starting from init. Primes will be indicated by prime char and #
# non-primes by composite char. The center of the spiral will be #
# indicated by center char - unless the center value is prime #
PROC print ulam spiral for primes = ( INT width, init, CHAR prime char, composite char, center char )VOID:
IF width >= 1 THEN
INT n = IF ODD width THEN width ELSE width + 1 FI;
[]BOOL prime = PRIMESIEVE ( init + ( n * n ) );
[ 1 : n, 1 : n ]CHAR spiral; FOR i TO n DO FOR j TO n DO spiral[ i, j ] := "_" OD OD;
INT y := ( n + 1 ) OVER 2;
INT x := y;
INT v := init;
spiral[ x, y ] := IF prime[ init ] THEN prime char ELSE center char FI;
INT w := 0;
WHILE x < 1 UPB spiral DO
w +:= 2;
x +:= 1;
y +:= 1;
FOR i TO w DO # right edge #
spiral[ x, y -:= 1 ] := IF prime[ v +:= 1 ] THEN prime char ELSE composite char FI
OD;
FOR i TO w DO # top edge #
spiral[ x -:= 1, y ] := IF prime[ v +:= 1 ] THEN prime char ELSE composite char FI
OD;
FOR i TO w DO # left edge #
spiral[ x, y +:= 1 ] := IF prime[ v +:= 1 ] THEN prime char ELSE composite char FI
OD;
FOR i TO w DO # bottom edge #
spiral[ x +:= 1, y ] := IF prime[ v +:= 1 ] THEN prime char ELSE composite char FI
OD
OD;
FOR v pos TO width DO
FOR h pos TO width DO
print( ( spiral[ h pos, v pos ] ) )
OD;
print( ( newline ) )
OD
FI # ulam spiral for primes # ;
 
print ulam spiral for primes( 35, 1, "#", " ", "+" )
END
</syntaxhighlight>
{{out}}
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</pre>
 
=={{header|C}}==
Line 1,275 ⟶ 1,361:
img.savePGM("ulam_spiral.pgm");
}</syntaxhighlight>
 
 
 
=={{header|Delphi}}==
{{works with|Delphi|6.0}}
{{libheader|SysUtils,StdCtrls}}
 
[[File:DelphiUlamPrimeSpiral.png|frame|none]]
 
 
<syntaxhighlight lang="Delphi">
 
 
 
 
procedure DrawMatrixPrimes(Image: TImage; Mat: TMatrix);
{Display spiral, only marking cells that contain prime numbers}
var X,Y: integer;
var S: string;
var Size,Step: integer;
var Off: TSize;
var R: TRect;
begin
{Calculate size of grid}
Size:=Min(Image.Width,Image.Height);
Step:=Size div Length(Mat);
{Draw border rectangle}
Image.Canvas.Brush.Color:=clGreen;
Image.Canvas.Pen.Width:=4;
Image.Canvas.Rectangle(2,2,Length(Mat)*Step,Length(Mat)*Step);
{Setup font}
Image.Canvas.Font.Name:='Arial';
Image.Canvas.Font.Style:=[fsBold];
Image.Canvas.Font.Size:=14;
{Draw grid}
Image.Canvas.Pen.Width:=1;
{Draw vertical lines}
for X:=0 to Length(Mat) do
begin
Image.Canvas.MoveTo(X*Step,0);
Image.Canvas.LineTo(X*Step,Step*Length(Mat));
end;
{Draw horizontal lines}
for Y:=0 to Length(Mat) do
begin
Image.Canvas.MoveTo(0,Y*Step);
Image.Canvas.LineTo(Step*Length(Mat),Y*Step);
end;
{Label cells that contain primes}
for Y:=0 to High(Mat[0]) do
for X:=0 to High(Mat) do
if IsPrime(trunc(Mat[X,Y])) then
begin
{Color cells}
R:=Rect((X*Step)+2,(Y*Step)+2,X*Step+Step,Y*Step+Step);
InflateRect(R,-1,-1);
Image.Canvas.Pen.Width:=4;
Image.Canvas.Pen.Color:=clBlue;
Image.Canvas.Brush.Color:=clLime;
Image.Canvas.Rectangle(R);
{Label cell}
S:=Format('%0.0f',[Mat[X,Y]]);
Off:=Image.Canvas.TextExtent(S);
Off.CX:=(Step-Off.CX) div 2;
Off.CY:=(Step-Off.CY) div 2;
Image.Canvas.TextOut(X*Step+Off.CX,Y*Step+Off.CY,S);
end;
Image.Invalidate;
end;
 
 
 
procedure MakeSqrSpiralMatrix(var Mat: TMatrix; MatSize: integer);
{Create a spiral matrix of specified size}
var Inx: integer;
var R: TRect;
 
 
 
procedure DoTopRect(Off1,Off2: integer);
{Do top part of rectangle}
var X,Y: integer;
begin
for X:=R.Left+Off1 to R.Right+Off2 do
begin
Mat[X,R.Top]:=Inx;
Dec(Inx);
end;
end;
 
procedure DoRightRect(Off1,Off2: integer);
{Do Right part of rectangle}
var X,Y: integer;
begin
for Y:=R.Top+Off1 to R.Bottom+Off2 do
begin
Mat[R.Right,Y]:=Inx;
Dec(Inx);
end;
end;
 
 
procedure DoBottomRect(Off1,Off2: integer);
{Do bottom part of rectangle}
var X,Y: integer;
begin
for X:= R.Right+Off1 downto R.Left+Off2 do
begin
Mat[X,R.Bottom]:=Inx;
Dec(Inx);
end;
end;
 
procedure DoLeftRect(Off1,Off2: integer);
{Do left part of rectangle}
var X,Y: integer;
begin
for Y:=R.Bottom+Off1 downto R.Top+Off2 do
begin
Mat[R.Left,Y]:=Inx;
Dec(Inx);
end;
end;
 
 
procedure DoRect(R: TRect; var Inx: integer);
{Create one rotation of spiral around the rectangle}
begin
{The orientation of spiral is based in the size}
if (MatSize and 1)=0 then
begin
{Handle even sizes}
DoTopRect(0,0);
DoRightRect(1,0);
DoBottomRect(-1,0);
DoLeftRect(-1,1);
end
else
begin
{Handle odd sizes}
DoBottomRect(0,0);
DoLeftRect(-1,0);
DoTopRect(1,0);
DoRightRect(1,-1);
end
end;
 
 
 
begin
{Set matrix size}
SetLength(Mat,MatSize,MatSize);
{create matching rectangle}
R:=Rect(0,0,MatSize-1,MatSize-1);
Inx:=MatSize*MatSize;
{draw spiral around retangle and deflate rectanle until spiral is done}
while (R.Left<=R.Right) and (R.Top<=R.Bottom) do
begin
DoRect(R,Inx);
InflateRect(R,-1,-1);
end;
end;
 
 
 
procedure UlamPrimeSpiral(Image: TImage);
var Mat: TMatrix;
begin
MakeSqrSpiralMatrix(Mat,9);
DrawMatrixPrimes(Image,Mat);
end;
 
 
 
</syntaxhighlight>
{{out}}
<pre>
 
Elapsed Time: 1.550 ms.
 
</pre>
 
=={{header|EasyLang}}==
 
[https://easylang.dev/show/#cod=bZHdUsMgEIXveYqd8c5OmdTaC2eap0mIoglEIDX49LILi0w1F4HDfucsP9NmBtB+dXoBsy0gBQDoieZXeEKVPqfC5gx0KDMBfS5+velZJXntwX+6gL7iKSGLHYnuyvJdGgdS5qGHU21RqJOQwgAW9vS/dCLmYdxpcYyU/QBidXYAssh6igLlfBLclHxUUTOCsQVjC6Lr2JC/+t9MRr1qkb/RMp2LtuyDWnnLpl7BjrNkfcwykowsF3tTCYnlmPx+TaNBuyE9TCcv3CyoPXj9reAsqn02r3x9k3XwAcHC8ws6cFc4InEob42XiyOi74hi8VhbskUyo5E5lyqb7/xlqbFzAu75Bw== Run it]
 
<syntaxhighlight>
func isprim num .
if num < 2
return 0
.
i = 2
while i <= sqrt num
if num mod i = 0
return 0
.
i += 1
.
return 1
.
n = 1
x = 50
y = 50
dx = 1
dy = 0
#
proc turn . .
if dx = 1
dx = 0
dy = 1
elif dy = 1
dy = 0
dx = -1
elif dx = -1
dx = 0
dy = -1
else
dx = 1
dy = 0
.
.
proc step . .
n += 1
x += dx * 1
y += dy * 1
move x y
if isprim n = 1
circle 0.5
.
.
textsize 3
move x y
lng = 0
#
for k to 49
step
lng += 2
turn
for j to lng - 1
step
.
for i to 3
turn
for j to lng
step
.
.
.
</syntaxhighlight>
 
 
=={{header|EchoLisp}}==
Line 1,991 ⟶ 2,327:
=={{header|Fōrmulæ}}==
 
{{FormulaeEntry|page=https://formulae.org/?script=examples/Ulam_spiral}}
Fōrmulæ programs are not textual, visualization/edition of programs is done showing/manipulating structures but not text. Moreover, there can be multiple visual representations of the same program. Even though it is possible to have textual representation &mdash;i.e. XML, JSON&mdash; they are intended for storage and transfer purposes more than visualization and edition.
 
'''Solution'''
Programs in Fōrmulæ are created/edited online in its [https://formulae.org website], However they run on execution servers. By default remote servers are used, but they are limited in memory and processing power, since they are intended for demonstration and casual use. A local server can be downloaded and installed, it has no limitations (it runs in your own computer). Because of that, example programs can be fully visualized and edited, but some of them will not run if they require a moderate or heavy computation/memory resources, and no local server is being used.
 
[[File:Fōrmulæ - Ulam spiral 01.png]]
In '''[https://formulae.org/?example=Ulam_spiral this]''' page you can see the program(s) related to this task and their results.
 
'''Test case'''
 
[[File:Fōrmulæ - Ulam spiral 02.png]]
 
[[File:Fōrmulæ - Ulam spiral 03.png]]
 
=={{header|Go}}==
Line 3,063 ⟶ 3,405:
* * *
* * * * </pre>
 
=={{header|Maxima}}==
[[File:Ulam spiral.png|thumb|Ulam spiral powered by Maxima]]
Using the function defined in the Spiral matrix task
<syntaxhighlight lang="maxima">
/* Adapting the spiral to the problem requirements */
spiral_from_center(n):=(n^2+1)*matrixmap(lambda([x],x+1),zeromatrix(n,n))-spiral(n)$
 
/* Testing */
spiral_from_center(35)$
matrixmap(lambda([x],if primep(x) then "O" else ""),%);
</syntaxhighlight>
 
=={{header|Nim}}==
Line 4,181 ⟶ 4,535:
- 43 - - - 47 - - -
73 - - - - - 79 - -
</pre>
 
=={{header|Quackery}}==
 
<code>spiral</code> is defined at [[Spiral matrix#Quackery]].
 
<code>isprime</code> is defined at [[Primality by trial division#Quackery]].
 
<syntaxhighlight lang="Quackery"> 32 spiral
witheach
[ witheach
[ 1024 swap -
isprime iff
say " o"
else say " ." ]
cr ]</syntaxhighlight>
 
{{out}}
 
<pre>
. . . o . o . . . . . o . . . o . . . . . . . . . . . o . . . .
. . . . . . . . . . . . . . o . . . o . o . . . o . . . . . . .
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o . . . o . . . o . o . . . o . . . . . . . o . . . o . o . . .
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. o . o . o . o . o . o . o . . . o . . . . . . . o . . . . . .
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. . o . . . . . . . o . o . o . . . . . . . . . . . . . . . . .
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o . . . o . o . . . o . o . . . o . . . o . o . . . o . . . o .
. . . o . . . o . . . o . . . . . o . . . . . o . o . . . o . .
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. o . o . o . . . . . . . . . o . o . . . . . o . . . . . o . o
. . o . . . o . . . . . . . . . . . o . o . . . . . . . . . . .
. o . o . . . . . o . . . . . o . . . o . o . . . . . . . . . .
o . . . . . . . o . . . . . . . . . o . . . . . . . o . . . . .
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. . . . . . o . . . o . . . . . o . . . . . o . . . . . . . . .
</pre>
 
Line 5,399 ⟶ 5,805:
{{libheader|Wren-str}}
{{libheader|Wren-fmt}}
<syntaxhighlight lang="ecmascriptwren">import "./dynamic" for Enum
import "./math" for Int
import "./str" for Char
import "./fmt" for Fmt
 
var Direction = Enum.create("Direction", ["right", "up", "left", "down"])
Line 5,560 ⟶ 5,966:
 
http://www.zenkinetic.com/Images/RosettaCode/ulamSpiral.png
 
 
=={{header|ZX Spectrum Basic}}==
a simplistic naive procedure that on a real machine will take some DAYS at the max of 176x176 numbers to check
 
RUN 10 , to start
 
 
<syntaxhighlight lang="ZX Spectrum Basic">
 
1 IF n<max THEN LET n=n+1: FOR p=2 TO n-1: LET r= (INT (n/p)<>n/p): IF r THEN NEXT p
2 IF p=n THEN LET pr=pr+1: LET kx=(255-xx AND k<3)+(xx AND k>2): LET ky=(175-yy AND (k=1 OR k=3)+(yy AND (k=2 OR k=4))): PLOT kx,ky: PRINT #0;AT 0,0;n;" pr";pr
3 RETURN
10 CLS : PRINT "ULAM SPIRAL OF PRIME's"'''"it takes DAYS at max level"'"and 3.5MHz"
12 INPUT "square size= LxL"'"l: ";l: IF l<>INT l OR l<1 OR l>176 THEN GO TO 12
13 LET max=l*l: PRINT ''l;"x";l;"=";max;" positive integers"
15 INPUT "0,0 orientation 1-4: ";k: IF k<1 OR k>4 THEN GO TO 15
20 CLS : LET xx=127: LET yy=88: LET n=0: LET pr=0: PRINT #0;AT 0,15;max
40 FOR q=0 TO l: LET m=INT (q/2)=q/2: LET m=-1*m+NOT m
60 FOR x=0 TO q*m STEP m: GO SUB 1 : LET xx=xx+m: NEXT x
80 FOR y=0 TO q*m STEP m: GO SUB 1 : LET yy=yy+m: NEXT y: NEXT q
PureFox
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