⚠️ Warning: This is a draft ⚠️
This means it might contain formatting issues, incorrect code, conceptual problems, or other severe issues.
If you want to help to improve and eventually enable this page, please fork RosettaGit's repository and open a merge request on GitHub.
{{task}}
The [[wp:Archimedean_spiral|Archimedean spiral]] is a spiral named after the Greek mathematician Archimedes.
An Archimedean spiral can be described by the equation:
:
with real numbers ''a'' and ''b''.
;Task
Draw an Archimedean spiral.
AWK
# syntax: GAWK -f ARCHIMEDEAN_SPIRAL.AWK
# converted from Applesoft BASIC
BEGIN {
x_min = y_min = 9999
x_max = y_max = 0
h = 96
w = h + h / 2
a = 1
b = 1
m = 6 * 3.1415926
step = .02
for (t=step; t<=m; t+=step) { # build spiral
r = a + b * t
x = int(r * cos(t) + w)
y = int(r * sin(t) + h)
if (x <= 0 || y <= 0) { continue }
if (x >= 280 ) { continue }
if (y >= 192) { continue }
arr[x,y] = "*"
x_min = min(x_min,x)
x_max = max(x_max,x)
y_min = min(y_min,y)
y_max = max(y_max,y)
}
for (i=x_min; i<=x_max; i++) { # print spiral
rec = ""
for (j=y_min; j<=y_max; j++) {
rec = sprintf("%s%1s",rec,arr[i,j])
}
printf("%s\n",rec)
}
exit(0)
}
function max(x,y) { return((x > y) ? x : y) }
function min(x,y) { return((x < y) ? x : y) }
{{out}}
**********
*** ***
** **
** **
** **
** **
** ******* **
** *** *** *
* ** ** **
** ** ** *
* ** ** **
** ** * *
* * **** * *
* * *** ** * **
** * * ** * *
* * ** * * *
* * * * * *
* ** * ** * *
* ** * ** * **
* * * ** *
* * * * *
** * * ** **
* * ** ** *
* * *** *** **
** ** ****** *
* * **
* ** **
* ** **
** ** **
* **** ***
* ********
*
*
**
***
****
*****
BASIC
=
Applesoft BASIC
=
110 LET H = 96
120 LET W = H + H / 2
130 HGR2
140 HCOLOR= 3
150 LET A = 1
160 LET B = 9
170 LET PI = 3.1415926535
180 LET M = 10 * PI
190 LET S = .02
200 FOR T = S TO M STEP S
210 LET R = A + B * T
220 LET X = R * COS (T) + W
230 LET Y = R * SIN (T) + H
240 IF X < 0 THEN 290
250 IF Y < 0 THEN 290
260 IF X > 279 THEN 290
270 IF Y > 191 THEN 290
280 HPLOT X,Y
290 NEXT
=
BASIC256
=
# Basic-256 ver 1.1.4
# Archimedean Spiral
width = 430 : height = 430
graphsize width, height
rect 0,0, graphwidth,graphheight
penwidth 1
color green
x = width/2 : y = height/2 # Center of graphics window
i = 1 : t = 0 : xn = 0 : yn = 0 # Initial values
iter = 150 : q = 30
line x,0,x,height
line 0,y,width,y
penwidth 2
color red
while i <= iter
t = i / q * pi
xn = (1 + (1 * t)) * cos(t) +x
yn = (1 + (1 * t)) * sin(t) +y
line x,y,xn,yn
x = xn : y = yn
print i + chr(9) + int(x) + chr(9) + int(y) + chr(9) + int(t) # chr(9) = TAB
i += 1
end while
imgsave "spiral-Basic-256.png", "PNG"
=
Commodore BASIC
= Commodore BASIC 2.0 lacks in-built graphics capability. This implementation is written for Commodore BASIC 7.0 that was built into the Commodore 128 computer. Should also work for Commodore BASIC 3.5.
1 REM ARCHIMEDEAN SPIRAL
2 REM USING COMMODORE BASIC 7.0
3 REM OF THE COMMODORE 128
4 REM **********************************
10 GRAPHIC 1,1
20 A = 1.5
30 B = 0.7
40 X0 = 160 : Y0 = 100
50 FOR T = 0 TO 40*π STEP 0.2
60 R = A+B*T
70 X = R*COS(T)+160 : Y = R*SIN(T)+100
80 DRAW 1,X0,Y0 TO X,Y
90 X0 = X : Y0 = Y
100 NEXT T
110 GOTO 110
=
FreeBASIC
=
' version 16-10-2016
' compile with: fbc -s gui
Const As double deg2rad = Atn(1) * 4 / 180 ' pi = atn(1) * 4, pi/180
Const As UInteger screensize = 600 ' size of window in pixels
Const As Double turns = 5 ' number of turns
Const As UInteger halfscrn = screensize \ 2
Const As uinteger sf = (turns * (screensize - 100)) / halfscrn
ScreenRes screensize, screensize, 32 ' screen 600 * 600 pixels, 4 byte color
Dim As Double r, x, y
For r = 0 To turns * 360 Step 0.05
x = Cos(r * deg2rad) * r / sf
y = Sin(r * deg2rad) * r / sf
PSet(halfscrn + x, halfscrn - y), RGB(255, 255, 255)
Next
' empty keyboard buffer
While InKey <> "" : Wend
Print : Print "hit any key to end program"
Sleep
End
==={{header|IS-BASIC}}===
=
## Run BASIC
=
```Run BASIC
'archimedean spiral.bas
'runs in Run Basic
'Run Basic website http://www.runbasic.com
'From Rosettacode.org/wiki/ *** Liberty_BASIC
graphic #g, 300,300 'width and height - the center is 150
c = 255 '255 for white '0 for black
print "Welcome to the Arch-Spiral Program"
pi=acs(-1)
nLoops = 5
#g cls("blue") 'blue background color
#g color(c,c,c) 'set line color - see color above
for t=0 to 2*pi*nLoops step 0.01
'c = c - 1 'changes color parameter
x=100*t/(2*pi*nLoops)*cos(t)+150 '150x150 is the center
y=100*t/(2*pi*nLoops)*sin(t)+150
#g color(c,c,c) 'changes color
#g set(x,y)
'if c <1 then c=255
next
render #g
print "Thank you and Goodbye"
end
End
=
QBASIC
=
SCREEN 12
WINDOW (-2.67, -2!)-(2.67, 2!)
PI = 4 * ATN(1)
H = PI / 40
A = .2: B = .05
PSET (A, 0)
FOR I = 0 TO 400
T = I * H
X = (A + B * T) * COS(T)
Y = (A + B * T) * SIN(T)
LINE -(X, Y)
NEXT
=
Sinclair ZX81 BASIC
= {{trans|Applesoft BASIC}} Works with the unexpanded (1k RAM) ZX81. The output is quite blocky, but identifiably a spiral.
10 LET A=1.5
20 LET B=0.7
30 FOR T=0 TO 7*PI STEP 0.05
40 LET R=A+B*T
50 PLOT R*COS T+32,R*SIN T+22
60 NEXT T
{{out}} Screenshot [http://edmundgriffiths.com/zx81archspiral.jpg here].
C
Interactive code which asks the parameters a and b as inputs, the number of cycles and the division steps. Requires the [http://www.cs.colorado.edu/~main/bgi/cs1300/ WinBGIm] library.
#include<graphics.h> #include<stdio.h> #include<math.h> #define pi M_PI int main(){ double a,b,cycles,incr,i; int steps,x=500,y=500; printf("Enter the parameters a and b : "); scanf("%lf%lf",&a,&b); printf("Enter cycles : "); scanf("%lf",&cycles); printf("Enter divisional steps : "); scanf("%d",&steps); incr = 1.0/steps; initwindow(1000,1000,"Archimedean Spiral"); for(i=0;i<=cycles*pi;i+=incr){ putpixel(x + (a + b*i)*cos(i),x + (a + b*i)*sin(i),15); } getch(); closegraph(); }
C++
[[File:SpiralCpp.png|200px|thumb|right]]
#include <windows.h> #include <string> #include <iostream> const int BMP_SIZE = 600; class myBitmap { public: myBitmap() : pen( NULL ), brush( NULL ), clr( 0 ), wid( 1 ) {} ~myBitmap() { DeleteObject( pen ); DeleteObject( brush ); DeleteDC( hdc ); DeleteObject( bmp ); } bool create( int w, int h ) { BITMAPINFO bi; ZeroMemory( &bi, sizeof( bi ) ); bi.bmiHeader.biSize = sizeof( bi.bmiHeader ); bi.bmiHeader.biBitCount = sizeof( DWORD ) * 8; bi.bmiHeader.biCompression = BI_RGB; bi.bmiHeader.biPlanes = 1; bi.bmiHeader.biWidth = w; bi.bmiHeader.biHeight = -h; HDC dc = GetDC( GetConsoleWindow() ); bmp = CreateDIBSection( dc, &bi, DIB_RGB_COLORS, &pBits, NULL, 0 ); if( !bmp ) return false; hdc = CreateCompatibleDC( dc ); SelectObject( hdc, bmp ); ReleaseDC( GetConsoleWindow(), dc ); width = w; height = h; return true; } void clear( BYTE clr = 0 ) { memset( pBits, clr, width * height * sizeof( DWORD ) ); } void setBrushColor( DWORD bClr ) { if( brush ) DeleteObject( brush ); brush = CreateSolidBrush( bClr ); SelectObject( hdc, brush ); } void setPenColor( DWORD c ) { clr = c; createPen(); } void setPenWidth( int w ) { wid = w; createPen(); } void saveBitmap( std::string path ) { BITMAPFILEHEADER fileheader; BITMAPINFO infoheader; BITMAP bitmap; DWORD wb; GetObject( bmp, sizeof( bitmap ), &bitmap ); DWORD* dwpBits = new DWORD[bitmap.bmWidth * bitmap.bmHeight]; ZeroMemory( dwpBits, bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ) ); ZeroMemory( &infoheader, sizeof( BITMAPINFO ) ); ZeroMemory( &fileheader, sizeof( BITMAPFILEHEADER ) ); infoheader.bmiHeader.biBitCount = sizeof( DWORD ) * 8; infoheader.bmiHeader.biCompression = BI_RGB; infoheader.bmiHeader.biPlanes = 1; infoheader.bmiHeader.biSize = sizeof( infoheader.bmiHeader ); infoheader.bmiHeader.biHeight = bitmap.bmHeight; infoheader.bmiHeader.biWidth = bitmap.bmWidth; infoheader.bmiHeader.biSizeImage = bitmap.bmWidth * bitmap.bmHeight * sizeof( DWORD ); fileheader.bfType = 0x4D42; fileheader.bfOffBits = sizeof( infoheader.bmiHeader ) + sizeof( BITMAPFILEHEADER ); fileheader.bfSize = fileheader.bfOffBits + infoheader.bmiHeader.biSizeImage; GetDIBits( hdc, bmp, 0, height, ( LPVOID )dwpBits, &infoheader, DIB_RGB_COLORS ); HANDLE file = CreateFile( path.c_str(), GENERIC_WRITE, 0, NULL, CREATE_ALWAYS, FILE_ATTRIBUTE_NORMAL, NULL ); WriteFile( file, &fileheader, sizeof( BITMAPFILEHEADER ), &wb, NULL ); WriteFile( file, &infoheader.bmiHeader, sizeof( infoheader.bmiHeader ), &wb, NULL ); WriteFile( file, dwpBits, bitmap.bmWidth * bitmap.bmHeight * 4, &wb, NULL ); CloseHandle( file ); delete [] dwpBits; } HDC getDC() const { return hdc; } int getWidth() const { return width; } int getHeight() const { return height; } private: void createPen() { if( pen ) DeleteObject( pen ); pen = CreatePen( PS_SOLID, wid, clr ); SelectObject( hdc, pen ); } HBITMAP bmp; HDC hdc; HPEN pen; HBRUSH brush; void *pBits; int width, height, wid; DWORD clr; }; class spiral { public: spiral() { bmp.create( BMP_SIZE, BMP_SIZE ); } void draw( int c, int s ) { double a = .2, b = .3, r, x, y; int w = BMP_SIZE >> 1; HDC dc = bmp.getDC(); for( double d = 0; d < c * 6.28318530718; d += .002 ) { r = a + b * d; x = r * cos( d ); y = r * sin( d ); SetPixel( dc, ( int )( s * x + w ), ( int )( s * y + w ), 255 ); } // saves the bitmap bmp.saveBitmap( "./spiral.bmp" ); } private: myBitmap bmp; }; int main(int argc, char* argv[]) { spiral s; s.draw( 16, 8 ); return 0; }
C#
using System; using System.Linq; using System.Drawing; using System.Diagnostics; using System.Drawing.Drawing2D; class Program { const int width = 380; const int height = 380; static PointF archimedeanPoint(int degrees) { const double a = 1; const double b = 9; double t = degrees * Math.PI / 180; double r = a + b * t; return new PointF { X = (float)(width / 2 + r * Math.Cos(t)), Y = (float)(height / 2 + r * Math.Sin(t)) }; } static void Main(string[] args) { var bm = new Bitmap(width, height); var g = Graphics.FromImage(bm); g.SmoothingMode = SmoothingMode.AntiAlias; g.FillRectangle(new SolidBrush(Color.White), new Rectangle { X = 0, Y = 0, Width = width, Height = height }); var pen = new Pen(Color.OrangeRed, 1.5f); var spiral = Enumerable.Range(0, 360 * 3).AsParallel().AsOrdered().Select(archimedeanPoint); var p0 = new PointF(width / 2, height / 2); foreach (var p1 in spiral) { g.DrawLine(pen, p0, p1); p0 = p1; } g.Save(); // is this really necessary ? bm.Save("archimedes-csharp.png"); Process.Start("archimedes-csharp.png"); // Launches default photo viewing app } }
Common Lisp
Common Lisp doesn't provide native graphical output. Libraries or bitmapped output could be used instead, but for this solution, the output is accomplished with character printing.
(defun draw-coords-as-text (coords size fill-char) (let* ((min-x (apply #'min (mapcar #'car coords))) (min-y (apply #'min (mapcar #'cdr coords))) (max-x (apply #'max (mapcar #'car coords))) (max-y (apply #'max (mapcar #'cdr coords))) (real-size (max (+ (abs min-x) (abs max-x)) ; bounding square (+ (abs min-y) (abs max-y)))) (scale-factor (* (1- size) (/ 1 real-size))) (center-x (* scale-factor -1 min-x)) (center-y (* scale-factor -1 min-y)) (intermediate-result (make-array (list size size) :element-type 'char :initial-element #\space))) (dolist (c coords) (let ((final-x (floor (+ center-x (* scale-factor (car c))))) (final-y (floor (+ center-y (* scale-factor (cdr c)))))) (setf (aref intermediate-result final-x final-y) fill-char))) ; print results to output (loop for i below (array-total-size intermediate-result) do (when (zerop (mod i size)) (terpri)) (princ (row-major-aref intermediate-result i))))) (defun spiral (a b step-resolution step-count) "Returns a list of coordinates for r=a+b*theta stepping theta by step-resolution" (loop for theta from 0 upto (* step-count step-resolution) by step-resolution for r = (+ a (* b theta)) for x = (* r (cos theta)) for y = (* r (sin theta)) collect (cons x y))) (draw-coords-as-text (spiral 10 10 0.01 1500) 30 #\*) ; Output: ; ; * ; ****** * ; **** *** ** ; *** ** * ; ** ** * ; ** ** * ; * ** ** ; ** * * ; ** ****** * * ; * ** ** ** * ; * ** * * * ; * ** * * ** ; * * * * * ; * * * ** * * ; * * *** ** * ; * ** * * ; * * ** * ; * ** ** ** ; ** ** ** * ; * ** ** ** ; ** ******** * ; * ** ; ** ** ; ** ** ; ** *** ; ** ** ; **** *** ; ******* ;
Clojure
{{Works with| Incanter}}
(use '(incanter core stats charts io)) (defn Arquimidean-function [a b theta] (+ a (* theta b))) (defn transform-pl-xy [r theta] (let [x (* r (sin theta)) y (* r (cos theta))] [x y])) (defn arq-spiral [t] (transform-pl-xy (Arquimidean-function 0 7 t) t)) (view (parametric-plot arq-spiral 0 (* 10 Math/PI)))
Frege
{{trans|Java}} {{Works with|Frege|3.23.888}}
module Archimedean where
import Java.IO
import Prelude.Math
data BufferedImage = native java.awt.image.BufferedImage where
pure native type_3byte_bgr "java.awt.image.BufferedImage.TYPE_3BYTE_BGR" :: Int
native new :: Int -> Int -> Int -> STMutable s BufferedImage
native createGraphics :: Mutable s BufferedImage -> STMutable s Graphics2D
data Color = pure native java.awt.Color where
pure native orange "java.awt.Color.orange" :: Color
pure native white "java.awt.Color.white" :: Color
pure native new :: Int -> Color
data BasicStroke = pure native java.awt.BasicStroke where
pure native new :: Float -> BasicStroke
data RenderingHints = native java.awt.RenderingHints where
pure native key_antialiasing "java.awt.RenderingHints.KEY_ANTIALIASING" :: RenderingHints_Key
pure native value_antialias_on "java.awt.RenderingHints.VALUE_ANTIALIAS_ON" :: Object
data RenderingHints_Key = pure native java.awt.RenderingHints.Key
data Graphics2D = native java.awt.Graphics2D where
native drawLine :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native drawOval :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native fillRect :: Mutable s Graphics2D -> Int -> Int -> Int -> Int -> ST s ()
native setColor :: Mutable s Graphics2D -> Color -> ST s ()
native setRenderingHint :: Mutable s Graphics2D -> RenderingHints_Key -> Object -> ST s ()
native setStroke :: Mutable s Graphics2D -> BasicStroke -> ST s ()
data ImageIO = mutable native javax.imageio.ImageIO where
native write "javax.imageio.ImageIO.write" :: MutableIO BufferedImage -> String -> MutableIO File -> IO Bool throws IOException
width = 640
center = width `div` 2
roundi = fromIntegral . round
drawGrid :: Mutable s Graphics2D -> ST s ()
drawGrid g = do
g.setColor $ Color.new 0xEEEEEE
g.setStroke $ BasicStroke.new 2
let angle = toRadians 45
margin = 10
numRings = 8
spacing = (width - 2 * margin) `div` (numRings * 2)
forM_ [0 .. numRings-1] $ \i -> do
let pos = margin + i * spacing
size = width - (2 * margin + i * 2 * spacing)
ia = fromIntegral i * angle
multiplier = fromIntegral $ (width - 2 * margin) `div` 2
x2 = center + (roundi (cos ia * multiplier))
y2 = center - (roundi (sin ia * multiplier))
g.drawOval pos pos size size
g.drawLine center center x2 y2
drawSpiral :: Mutable s Graphics2D -> ST s ()
drawSpiral g = do
g.setStroke $ BasicStroke.new 2
g.setColor $ Color.orange
let degrees = toRadians 0.1
end = 360 * 2 * 10 * degrees
a = 0
b = 20
c = 1
drSp theta = do
let r = a + b * theta ** (1 / c)
x = r * cos theta
y = r * sin theta
theta' = theta + degrees
plot g (center + roundi x) (center - roundi y)
when (theta' < end) (drSp (theta' + degrees))
drSp 0
plot :: Mutable s Graphics2D -> Int -> Int -> ST s ()
plot g x y = g.drawOval x y 1 1
main = do
buffy <- BufferedImage.new width width BufferedImage.type_3byte_bgr
g <- buffy.createGraphics
g.setRenderingHint RenderingHints.key_antialiasing RenderingHints.value_antialias_on
g.setColor Color.white
g.fillRect 0 0 width width
drawGrid g
drawSpiral g
f <- File.new "SpiralFrege.png"
void $ ImageIO.write buffy "png" f
Output is [http://funwithsoftware.org/images/2016-SpiralFrege.png here] due to [[User talk:Short Circuit#Is file uploading blocked forever?|Is file uploading blocked forever?]]
Go
{{works with|go|1.9}} Creates a PNG file using only built-in packages.
package main import ( "image" "image/color" "image/draw" "image/png" "log" "math" "os" ) func main() { const ( width, height = 600, 600 centre = width / 2.0 degreesIncr = 0.1 * math.Pi / 180 turns = 2 stop = 360 * turns * 10 * degreesIncr fileName = "spiral.png" ) img := image.NewNRGBA(image.Rect(0, 0, width, height)) // create new image bg := image.NewUniform(color.RGBA{255, 255, 255, 255}) // prepare white for background draw.Draw(img, img.Bounds(), bg, image.ZP, draw.Src) // fill the background fgCol := color.RGBA{255, 0, 0, 255} // red plot a := 1.0 b := 20.0 for theta := 0.0; theta < stop; theta += degreesIncr { r := a + b*theta x := r * math.Cos(theta) y := r * math.Sin(theta) img.Set(int(centre+x), int(centre-y), fgCol) } imgFile, err := os.Create(fileName) if err != nil { log.Fatal(err) } defer imgFile.Close() if err := png.Encode(imgFile, img); err != nil { imgFile.Close() log.Fatal(err) } }
Haskell
{{works with|GHC|7.8.3}} {{works with|GHC|8.0.1}} {{libheader|Juicy.Pixels}} {{libheader|Rasterific}}
#!/usr/bin/env stack -- stack --resolver lts-7.0 --install-ghc runghc --package Rasterific --package JuicyPixels import Codec.Picture( PixelRGBA8( .. ), writePng ) import Graphics.Rasterific import Graphics.Rasterific.Texture import Graphics.Rasterific.Transformations archimedeanPoint a b t = V2 x y where r = a + b * t x = r * cos t y = r * sin t main :: IO () main = do let white = PixelRGBA8 255 255 255 255 drawColor = PixelRGBA8 0xFF 0x53 0x73 255 size = 800 points = map (archimedeanPoint 0 10) [0, 0.01 .. 60] hSize = fromIntegral size / 2 img = renderDrawing size size white $ withTransformation (translate $ V2 hSize hSize) $ withTexture (uniformTexture drawColor) $ stroke 4 JoinRound (CapRound, CapRound) $ polyline points writePng "SpiralHaskell.png" img
Output is [http://funwithsoftware.org/images/2016-SpiralHaskell.png here] due to [[User talk:Short Circuit#Is file uploading blocked forever?|Is file uploading blocked forever?]]
J
[[File:Archimedian spiral j.png|200px|thumb|right]]
require'plot'
'aspect 1' plot (*^)j.0.01*i.1400
Java
[[File:archimedian_spiral.png|300px|thumb|right]] {{works with|Java|8}}
import java.awt.*; import static java.lang.Math.*; import javax.swing.*; public class ArchimedeanSpiral extends JPanel { public ArchimedeanSpiral() { setPreferredSize(new Dimension(640, 640)); setBackground(Color.white); } void drawGrid(Graphics2D g) { g.setColor(new Color(0xEEEEEE)); g.setStroke(new BasicStroke(2)); double angle = toRadians(45); int w = getWidth(); int center = w / 2; int margin = 10; int numRings = 8; int spacing = (w - 2 * margin) / (numRings * 2); for (int i = 0; i < numRings; i++) { int pos = margin + i * spacing; int size = w - (2 * margin + i * 2 * spacing); g.drawOval(pos, pos, size, size); double ia = i * angle; int x2 = center + (int) (cos(ia) * (w - 2 * margin) / 2); int y2 = center - (int) (sin(ia) * (w - 2 * margin) / 2); g.drawLine(center, center, x2, y2); } } void drawSpiral(Graphics2D g) { g.setStroke(new BasicStroke(2)); g.setColor(Color.orange); double degrees = toRadians(0.1); double center = getWidth() / 2; double end = 360 * 2 * 10 * degrees; double a = 0; double b = 20; double c = 1; for (double theta = 0; theta < end; theta += degrees) { double r = a + b * pow(theta, 1 / c); double x = r * cos(theta); double y = r * sin(theta); plot(g, (int) (center + x), (int) (center - y)); } } void plot(Graphics2D g, int x, int y) { g.drawOval(x, y, 1, 1); } @Override public void paintComponent(Graphics gg) { super.paintComponent(gg); Graphics2D g = (Graphics2D) gg; g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON); drawGrid(g); drawSpiral(g); } public static void main(String[] args) { SwingUtilities.invokeLater(() -> { JFrame f = new JFrame(); f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE); f.setTitle("Archimedean Spiral"); f.setResizable(false); f.add(new ArchimedeanSpiral(), BorderLayout.CENTER); f.pack(); f.setLocationRelativeTo(null); f.setVisible(true); }); } }
JavaScript
{{Works with|Chrome}} [[File:ASjs.png|200px|right|thumb|Output ASjs.png]]
<!-- ArchiSpiral.html --> <html> <head><title>Archimedean spiral</title></head> <body onload="pAS(35,'navy');"> <h3>Archimedean spiral</h3> <p id=bo></p> <canvas id="canvId" width="640" height="640" style="border: 2px outset;"></canvas> <script> // Plotting Archimedean_spiral aev 3/17/17 // lps - number of loops, clr - color. function pAS(lps,clr) { var a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Math.PI,n=as/ai; var cvs=document.getElementById("canvId"); var ctx=cvs.getContext("2d"); ctx.fillStyle="white"; ctx.fillRect(0,0,cvs.width,cvs.height); var x=y=0, s=cvs.width/2; ctx.beginPath(); for (var i=1; i<n; i++) { x=r*Math.cos(a), y=r*Math.sin(a); ctx.lineTo(x+s,y+s); r+=ri; a+=ai; }//fend i ctx.strokeStyle = clr; ctx.stroke(); } </script></body></html>
{{Output}}
Page with Archimedean spiral like ASjs.png. Right-clicking on the canvas you can save
spiral as a png-file, for example.
Julia
{{works with|Julia|0.6}}
using UnicodePlots spiral(θ, a=0, b=1) = @. b * θ * cos(θ + a), b * θ * sin(θ + a) x, y = spiral(1:0.1:10) println(lineplot(x, y))
{{out}}
┌────────────────────────────────────────┐
10 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡆⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⣀⠤⠤⠤⠤⠤⠤⡧⠤⣀⣀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⢀⡠⠔⠊⠉⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠉⠓⠤⢄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⡠⠊⠁⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠉⠢⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⡠⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠘⢤⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⡜⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢇⠀⠀⠀⠀⠀⠀⠀│
│⠀⡸⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣀⠔⠊⠉⠉⠙⣧⡀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢸⠀⠀⠀⠀⠀⠀⠀│
│⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡴⠥⠤⠤⠤⠤⠤⡧⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⠤⡼⠤⠤⠤⠤⠤⠤⠄│
│⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⢣⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⣰⠁⠀⠀⠀⠀⠀⠀⠀│
│⠀⢇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⢆⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⣀⠜⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠘⡄⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠉⠒⠤⣀⡀⡇⠀⠀⠀⣀⣀⠤⠔⠊⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠘⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠈⡏⠉⠉⠉⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
│⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
-10 │⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⡇⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀│
└────────────────────────────────────────┘
-10 10
Kotlin
{{trans|Java}}
// version 1.1.0 import java.awt.* import javax.swing.* class ArchimedeanSpiral : JPanel() { init { preferredSize = Dimension(640, 640) background = Color.white } private fun drawGrid(g: Graphics2D) { g.color = Color(0xEEEEEE) g.stroke = BasicStroke(2f) val angle = Math.toRadians(45.0) val w = width val center = w / 2 val margin = 10 val numRings = 8 val spacing = (w - 2 * margin) / (numRings * 2) for (i in 0 until numRings) { val pos = margin + i * spacing val size = w - (2 * margin + i * 2 * spacing) g.drawOval(pos, pos, size, size) val ia = i * angle val x2 = center + (Math.cos(ia) * (w - 2 * margin) / 2).toInt() val y2 = center - (Math.sin(ia) * (w - 2 * margin) / 2).toInt() g.drawLine(center, center, x2, y2) } } private fun drawSpiral(g: Graphics2D) { g.stroke = BasicStroke(2f) g.color = Color.magenta val degrees = Math.toRadians(0.1) val center = width / 2 val end = 360 * 2 * 10 * degrees val a = 0.0 val b = 20.0 val c = 1.0 var theta = 0.0 while (theta < end) { val r = a + b * Math.pow(theta, 1.0 / c) val x = r * Math.cos(theta) val y = r * Math.sin(theta) plot(g, (center + x).toInt(), (center - y).toInt()) theta += degrees } } private fun plot(g: Graphics2D, x: Int, y: Int) { g.drawOval(x, y, 1, 1) } override fun paintComponent(gg: Graphics) { super.paintComponent(gg) val g = gg as Graphics2D g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON) drawGrid(g) drawSpiral(g) } } fun main(args: Array<String>) { SwingUtilities.invokeLater { val f = JFrame() f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE f.title = "Archimedean Spiral" f.isResizable = false f.add(ArchimedeanSpiral(), BorderLayout.CENTER) f.pack() f.setLocationRelativeTo(null) f.isVisible = true } }
Maple
plots[polarplot](1+2*theta, theta = 0 .. 6*Pi)
Mathematica
The built-in function PolarPlot easily creates the desired plot
With[{a = 5, b = 4}, PolarPlot[a + b t, {t, 0, 10 Pi}]]
MATLAB
a = 1; b = 1; turns = 2; theta = 0:0.1:2*turns*pi; polarplot(theta, a + b*theta);
PARI/GP
Note: cartes2() can be found here on [[Polyspiral#PARI.2FGP| PARI/GP]] page. {{Works with|PARI/GP|2.7.4 and above}} [[File:ArchiSpiral1.png|right|thumb|Output ArchiSpiral1.png]] [[File:ArchiSpiral2.png|right|thumb|Output ArchiSpiral2.png]]
\\ The Archimedean spiral
\\ ArchiSpiral() - Where: lps is a number of loops, c is a direction 0/1
\\ (counter-clockwise/clockwise). 6/6/16 aev
\\ Note: cartes2() can be found here on
\\ http://rosettacode.org/wiki/Polyspiral#PARI.2FGP page.
ArchiSpiral(size,lps,c=0)={
my(a=.0,ai=.1,r=.0,ri=.1,as=lps*2*Pi,n=as/ai,x,y,vc,vx=List(.0),vy=vx);
if(c<0||c>1, c=0); if(c, ai*=-1);
print(" *** The Archimedean spiral: size=",size," loops=",lps," c=",c);
for(i=1, n, vc=cartes2(r,a); x=vc[1]; y=vc[2];
listput(vx,x); listput(vy,y);
r+=ri; a+=ai;
);\\fend i
plothraw(Vec(vx),Vec(vy));
}
{\\ Executing:
ArchiSpiral(640,5); \\ArchiSpiral1.png
ArchiSpiral(640,5,1); \\ArchiSpiral2.png
}
{{Output}}
> ArchiSpiral(640,5); \\ArchiSpiral1.png
*** The Archimedean spiral: size=640 loops=5 c=0
> ArchiSpiral(640,5,1); \\ArchiSpiral2.png
*** The Archimedean spiral: size=640 loops=5 c=1
Perl
{{trans|Perl 6}}
use Imager; use constant PI => 3.14159265; my ($w, $h) = (400, 400); my $img = Imager->new(xsize => $w, ysize => $h); for ($theta = 0; $theta < 52*PI; $theta += 0.025) { $x = $w/2 + $theta * cos($theta/PI); $y = $h/2 + $theta * sin($theta/PI); $img->setpixel(x => $x, y => $y, color => '#FF00FF'); } $img->write(file => 'Archimedean-spiral.png');
Perl 6
{{works with|Rakudo|2018.10}}
use Image::PNG::Portable;
my ($w, $h) = (400, 400);
my $png = Image::PNG::Portable.new: :width($w), :height($h);
(0, .025 ... 52*π).race.map: -> \Θ {
$png.set: |((cis( Θ / π ) * Θ).reals »+« ($w/2, $h/2))».Int, 255, 0, 255;
}
$png.write: 'Archimedean-spiral-perl6.png';
Phix
{{trans|zkl}} {{libheader|pGUI}}
--
-- demo\rosetta\Archimedean_spiral.exw
--
include pGUI.e
Ihandle dlg, canvas
cdCanvas cddbuffer, cdcanvas
function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)
integer a = 0, b = 5
integer {width, height} = IupGetIntInt(canvas, "DRAWSIZE")
integer {centerX,centerY} = sq_floor_div({width,height},2)
cdCanvasActivate(cddbuffer)
for deg=0 to 360*7 do
atom rad = deg*PI/180
atom r = rad*b + a
integer x = centerX + floor(r*cos(rad))
integer y = centerY + floor(r*sin(rad))
cdCanvasPixel(cddbuffer, x, y, #00FF00)
end for
cdCanvasFlush(cddbuffer)
return IUP_DEFAULT
end function
function map_cb(Ihandle ih)
cdcanvas = cdCreateCanvas(CD_IUP, ih)
cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
cdCanvasSetBackground(cddbuffer, CD_WHITE)
cdCanvasSetForeground(cddbuffer, CD_RED)
return IUP_DEFAULT
end function
function esc_close(Ihandle /*ih*/, atom c)
if c=K_ESC then return IUP_CLOSE end if
return IUP_CONTINUE
end function
procedure main()
IupOpen()
canvas = IupCanvas(NULL)
IupSetAttribute(canvas, "RASTERSIZE", "340x340") -- initial size
IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
dlg = IupDialog(canvas)
IupSetAttribute(dlg, "TITLE", "Archimedean spiral")
IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))
IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))
IupMap(dlg)
IupSetAttribute(canvas, "RASTERSIZE", NULL) -- release the minimum limitation
IupShowXY(dlg,IUP_CENTER,IUP_CENTER)
IupMainLoop()
IupClose()
end procedure
main()
Processing
float x, y, theta; void setup() { theta = 0; size(500,500); } void draw() { x = (width/2)+theta*cos(theta/PI); y = (height/2)+(theta)*sin(theta/PI); point(x,y); theta = theta + 0.025; }
PureBasic
#MAXLOOP = 7*360
#XCENTER = 640/2
#YCENTER = 480/2
#SCALAR = 200
If OpenWindow(0, 100, 200, 640, 480, "Archimedean spiral")
If CreateImage(0, 640, 480,24,RGB(255,255,255))
If StartDrawing(ImageOutput(0))
i.f=0.0
While i<=#MAXLOOP
x.f=#XCENTER+Cos(Radian(i))*#SCALAR*i/#MAXLOOP
y.f=#YCENTER+Sin(Radian(i))*#SCALAR*i/#MAXLOOP
Plot(x,y,RGB(50,50,50))
i+0.05
Wend
StopDrawing()
EndIf
EndIf
ImageGadget(0, 0, 0, 0, 0, ImageID(0))
Repeat : Event = WaitWindowEvent() : Until Event = #PB_Event_CloseWindow
EndIf
End
Python
Using the '''turtle''' module.
from turtle import * from math import * color("blue") down() for i in range(200): t = i / 20 * pi x = (1 + 5 * t) * cos(t) y = (1 + 5 * t) * sin(t) goto(x, y) up() done()
R
with(list(s=seq(0, 10 * pi, length.out=500)), plot((1 + s) * exp(1i * s), type="l"))
Racket
[[File:archemedian-spiral-racket.png]]
#lang racket/base
(require plot
racket/math)
;; x and y bounds set to centralise the circle
(define (archemedian-spiral-renderer2d a b θ/τ-max
#:samples (samples (line-samples)))
(define (f θ) (+ a (* b θ)))
(define max-dim (+ a (* θ/τ-max 2 pi b)))
(polar f
0 (* θ/τ-max 2 pi)
#:x-min (- max-dim)
#:x-max max-dim
#:y-min (- max-dim)
#:y-max max-dim
#:samples samples))
(plot (list (archemedian-spiral-renderer2d 0.0 24 4)))
;; writes to a file so hopefully, I can post it to RC...
(plot-file (list (archemedian-spiral-renderer2d 0.0 24 4))
"images/archemidian-spiral-racket.png")
REXX
This REXX version allows the user to specify (or override) the various constants used to calculate and display the spiral (plot).
Note: the value of ''a'' doesn't mean that much as the plot is automatically centered.
/*REXX pgm plots several cycles (half a spiral) of the Archimedean spiral (ASCII plot).*/
parse arg cy a b inc chr . /*obtain optional arguments from the CL*/
if cy=='' | cy=="," then cy= 3 /*Not specified? Then use the default.*/
if a=='' | a=="," then a= 1 /* " " " " " " */
if b=='' | b=="," then b= 9 /* " " " " " " */
if inc=='' | inc=="," then inc= 0.02 /* " " " " " " */
if chr=='' | chr=="," then chr= '∙' /* " " " " " " */
if length(chr)==3 then chr= d2c(chr) /*plot character coded in decimal? */
if length(chr)==2 then chr= x2c(chr) /* " " " " hexadecimal? */
cy= max(2, cy); LOx= . /*set the LOx variable (a semaphore).*/
parse value scrsize() with sd sw . /*get the size of the terminal screen. */
w= sw - 1 ; mw= w * (cy-1) * 4 /*set useable width; max width for calc*/
h= sd - 1 + cy*10; mh= h * (cy-1) /* " " depth; " depth " " */
@.= /*initialize the line based plot field.*/
do t=1 to pi()*cy by inc /*calc all the coördinates for spiral. */
r= a + b* t /* " " " R " " */
x= w + r*cos(t); xx= x % 2 /* " " " X " " */
y= h + r*sin(t); yy= y % 2 /* " " " Y " " */
if x<0 | y<0 | x>mw | y>mh then iterate /*Is X or Y out of bounds? Then skip.*/
if LOx==. then do; LOx=xx; HIx=xx; LOy=yy; HIy=yy
end /* [↑] find the minimums and maximums.*/
LOx= min(LOx, xx); HIx= max(HIx, xx) /*determine the X MIN and MAX. */
LOy= min(LOy, yy); HIy= max(HIy, yy) /* " " Y " " " */
@.yy= overlay(chr, @.yy, xx+1) /*assign the plot character (glyph). */
end /*t*/
call plot /*invoke plotting subroutine (to term).*/
exit /*stick a fork in it, we're all done. */
/*──────────────────────────────────────────────────────────────────────────────────────*/
pi: pi=3.1415926535897932384626433832795028841971693993751058209749445923078; return pi
plot: do row=HIy to LOy by -1; say substr(@.row, LOx+1); end; return
r2r: return arg(1) // (pi() * 2) /*normalize radians ───► a unit circle.*/
/*──────────────────────────────────────────────────────────────────────────────────────*/
cos: procedure; parse arg x; x= r2r(x); a= abs(x); hpi= pi * .5
numeric fuzz min(6, digits() - 3); if a=pi then return -1
if a=hpi | a=hpi*3 then return 0 if a=pi / 3 then return .5
if a=pi * 2 / 3 then return -.5; return .sinCos(1, -1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
sin: procedure; parse arg x; x= r2r(x); numeric fuzz min(5, max(1, digits() -3))
if x=pi * .5 then return 1; if x==pi*1.5 then return -1
if abs(x)=pi | x=0 then return 0; return .sinCos(x, 1)
/*──────────────────────────────────────────────────────────────────────────────────────*/
.sinCos: parse arg z 1 _,i; q= x*x
do k=2 by 2 until p=z; p= z; _= -_*q/(k*(k+i)); z= z+_; end; return z
{{out|output|text= when using the following inputs: 13 , 5 , db }}
(Output is shown at '''1/20''' size.)
█ █ █ ██ █
█ █ █ █ █ █ █ █ █ █
█ █ █ █ █
█ █ █ █ █
█ █ █
█ █ █ █
█ █ █
█ █
█ █ █
█ ██
█ █
█ █
█ █
█ █
█ █
█ █
█ █ █ ██ █ ██ █ ██ █ █
█ ██ █ █ ██ █ █ █
█ █ ██ █ ██ █
█ ██ █ █ █
█ █ █ █ █
█ █ █ █ █
█ █ █ █ █
█ ██ █ █
█ █ ██ █
█ █ █
██ █ █
█ █ █ █
█ █ █ █ █
█ █
█ █ █ █
█ █ █ █
█ █ ███ ███ ███ ███ ███ █ █
█ █ ███ ███ █ █
█ █ █ ██ ██ █ █ █
█ █ ██ ██ █ █
█ ██ █ ██ █
█ █ ██ █ █ █
█ ██ █ █ █ █
█ █ ██ ██ █
█ █ █ █
█ ██ ██ █ █
█ █ █ █ █
█ █ ██ █ █
█ █ █ █ █ █
█ █ █ █ █
█ █ ██ █
█ █ █ █████ █ █ █
█ █ ███████ ███████ █ █ █
█ █ ████ ████ █ █
█ █ █ ███ ████ █ █
█ █ ███ ██ █ █ █
█ █ █ ██ ███ █ █
█ ██ ██ █ █ █
█ █ █ ██ ██ █
█ █ █ █ █ █ █
█ █ ██ █ █ █ █
█ █ █ ██ █ █
█ █ █ ██ ██ █ █
█ █ █ █ █ █
█ █ ██ ██ █ █ █
█ █ █ █ █ █
█ ██ ██ █ █ █
█ █ █ █ ████████████ █ █ █ █
█ █ █████ ████ ██ █
█ █ █ ███ ████ █ █ █ █
█ █ █ ███ ███ █ █ █
█ █ █ █ ██ ███ █ █
█ █ ██ ██ █ █ █
█ █ █ ███ ██ █ █ █ █
█ █ ██ █ █ █
█ █ █ █ ██ ██ █ █ █ █
█ █ ██ █ ██ █ █ █
█ █ █ █ ██ █ █
█ █ █ ██ █ █ █ █
█ █ █ █ █ ██ █ █ █
█ █ █ ██ █ █ █
█ █ █ █ ██ █ █ █ █
█ ██ █ █ █ █ █
█ █ █ █ █ ████████████ █ █
█ █ █ █ ███ ███ █ █ █ █ █
█ █ █ █ ██ ███ █ ██ █ █
█ █ █ ██ ██ █ █ █ █
█ █ █ █ ██ ██ ██ █ █ █
█ █ █ █ ██ ██ █ █ █ █
█ █ █ █ █ ██ ██ █ █ █
█ █ ██ █ █ █ █ █ █
█ █ █ █ █ ██ █ █ █ █
█ █ ██ ██ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █
█ █ █ ██ ██ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █
█ █ █ █ ██ █ █ █ █
█ █ █ █ ██ █████ █ █ █ █
█ █ █ █ █ ███ ███ █ █ █ █ █
█ █ █ █ ██ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ █ ██ █ █ █
█ █ █ █ █ █ █ █ █ █ █ █ █
█ █ █ ██ █ █ █ █
█ █ █ █ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █ █ █
█ █ █ █ █ ██ █ █ █ █
█ █ █ █ █ █ █ █ █ █
█ █ █ █ ██ ██ █ █ █ █ █
█ █ █ █ █ ██ █ █ █ █
█ █ █ █ ██ █ █ █ █ █
█ █ █ █ █ ██ █ █ █ █ █
█ █ ██ ██ ██ █ █ █
█ █ █ █ ███ ███ ██ █ █ █ █
█ █ █ █ █ █████ █████ █ █ █ █
█ █ █ █ ███ ██ ██ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ █ ██ █ █
█ █ █ █ ██ █ █ █ █
█ █ █ █ █ █ █ █
█ █ █ █ ██ █ █ █ █
█ █ █ ██ █ █ █ █ █
█ █ █ ██ █ █ █
█ █ ██ ██ ██ █ █ █
█ █ █ ██ ██ ██ █ █
█ █ █ █ ██ ██ █ █ █ █
█ █ ██ ███ █ █
█ █ █ ██ ███ ████ ██ █ █ █
█ █ █ ████ ████ █ █ █
█ █ █ █ █████████████ █ █ █
█ █ █ ██ █ █ █
█ █ ██ █ █ █
█ █ █ █ ██ █ █
█ █ ██ █ █
█ █ ██ █ █ █ █
█ █ █ ██ █ █ █
█ ██ █ ██ █ █
█ █ █ ██ █ █ █ █
█ ██ ██ █ █
█ █ █ ██ █ █ █ █
█ █ █ ███ ███ █
█ █ ██ ██ █ █ █
█ █ █ ███ ████ █ █ █
█ ██ ████ ███ █ █
█ █ ██████ ██████ █ █
█ █ █ ██████████ █ █
█ █ ██ █ █
█ █ ██ █ █ █
█ █ █ █ █
█ ██ ██ █ █
█ █ █
█ █ ██ ██ █ █
█ █ █ █ █
█ █ ██ ██ █
█ █ ██ █ █ █ █
█ █ ██ ██ █ █
█ ██ ██ █
█ █ ███ ███ █ █
█ █ ██ █ ███ █ █
█ ████ ███ █ █
█ █ ██ ████ ██████ ██████ █
█ █ █ █
█ ██ █ █
█ █
█ █ █ █ █
█ █ █ █
█ ██ █ █
█ █ ██ █
██ █
█ █ ██ █
█ ██ █ █
█ █ █ ██ █
█ █ █ ██ █
█ ██ ██ █
█ ██ █ ██ █
█ █ ██ █ ██ ██ █
█ █ ██ ██ ██ ██ ██ ██ █
█ █
█ █
█ █
█ █ █
█ █
█ █
█ █ █
█ █ █
█ █
██ █ █
█ █ █
██ ██
█ █ █ █
██ █ ██ █
█ █ ██ █ █ █ █
█ █ █ ██ █ █ █ █
```
## Ring
```ring
/*
+---------------------------------------------------------------------------------------------------------
+ Program Name : Archimedean spiral
+---------------------------------------------------------------------------------------------------------
*/
Load "guilib.ring"
horzSize = 400
vertSize = 400
counter = 0 ### cycle thru colors
colorRed = new qcolor() { setrgb(255,000,000,255) }
colorGreen = new qcolor() { setrgb(000,255,000,255) }
colorBlue = new qcolor() { setrgb(000,000,255,255) }
colorYellow = new qcolor() { setrgb(255,255,000,255) }
penUseR = new qpen() { setcolor(colorRed) setwidth(1) }
penUseG = new qpen() { setcolor(colorGreen) setwidth(1) }
penUseB = new qpen() { setcolor(colorBlue) setwidth(1) }
penUseY = new qpen() { setcolor(colorYellow) setwidth(1) }
deg2rad = atan(1) * 4 / 180
screensize = 600
turns = 5
halfscrn = screensize / 2
sf = (turns * (screensize - 100)) / halfscrn
x = 1
y = 1
r = 0
inc = 0.50 ### control increment speed of r
New qapp
{
win1 = new qwidget()
{
setwindowtitle("Draw Spiral")
setgeometry(100,100,600,600)
label1 = new qlabel(win1)
{
setgeometry(10,10,600,600)
settext("")
}
Canvas = new qlabel(win1)
{
MonaLisa = new qPixMap2( 600,600)
color = new qcolor(){ setrgb(255,0,0,255) }
daVinci = new qpainter()
{
begin(MonaLisa)
penUse = new qpen() { setcolor(colorRed) setwidth(1) }
setpen(penUseR)
#endpaint() ### This will Stop the Painting
}
setpixmap(MonaLisa)
}
oTimer = new qTimer(win1)
{
setinterval(1) ### 1 millisecond
settimeoutevent("DrawCounter()")
start()
}
show() ### Will show Painting ONLY after exec
}
exec()
}
###
### ==============================================
Func DrawCounter()
x = cos(r * deg2rad) * r / sf
y = sin(r * deg2rad) * r / sf
r += inc ### 0.20 fast, 0.90 slow
if r >= turns * 360
r = inc
x = 1
y = 1
counter++
whichColor = counter % 4
See "whichColor: "+ whichColor +nl
if whichColor = 0 daVinci.setpen(penUseR) ok
if whichColor = 1 daVinci.setpen(penUseG) ok
if whichColor = 2 daVinci.setpen(penUseB) ok
if whichColor = 3 daVinci.setpen(penUseY) ok
ok
hpoint = halfscrn + x
ypoint = halfscrn - y
daVinci.drawpoint(hpoint, ypoint)
Canvas.setpixmap(MonaLisa) ### Need this setpixmap to display imageLabel
win1.show() ### Need this show to display imageLabel
return
```
## Rust
```rust
#[macro_use(px)]
extern crate bmp;
use bmp::{Image, Pixel};
use std::f64;
fn main() {
let width = 600u32;
let half_width = (width / 2) as i32;
let mut img = Image::new(width, width);
let draw_color = px!(255, 128, 128);
// Constants defining the spiral size.
let a = 1.0_f64;
let b = 9.0_f64;
// max_angle = number of spirals * 2pi.
let max_angle = 5.0_f64 * 2.0_f64 * f64::consts::PI;
let mut theta = 0.0_f64;
while theta < max_angle {
theta = theta + 0.002_f64;
let r = a + b * theta;
let x = (r * theta.cos()) as i32 + half_width;
let y = (r * theta.sin()) as i32 + half_width;
img.set_pixel(x as u32, y as u32, draw_color);
}
// Save the image
let _ = img.save("archimedean_spiral.bmp").unwrap_or_else(|e| panic!("Failed to save: {}", e));
}
```
## SAS
```sas
data xy;
h=constant('pi')/40;
do i=0 to 400;
t=i*h;
x=(1+t)*cos(t);
y=(1+t)*sin(t);
output;
end;
keep x y;
run;
proc sgplot;
series x=x y=y;
run;
```
## Scala
### Java Swing Interoperability
```Scala
object ArchimedeanSpiral extends App {
SwingUtilities.invokeLater(() =>
new JFrame("Archimedean Spiral") {
class ArchimedeanSpiral extends JPanel {
setPreferredSize(new Dimension(640, 640))
setBackground(Color.white)
private def drawGrid(g: Graphics2D): Unit = {
val (angle, margin, numRings) = (toRadians(45), 10, 8)
val w = getWidth
val (center, spacing) = (w / 2, (w - 2 * margin) / (numRings * 2))
g.setColor(new Color(0xEEEEEE))
for (i <- 0 until numRings) {
val pos = margin + i * spacing
val size = w - (2 * margin + i * 2 * spacing)
g.drawOval(pos, pos, size, size)
val ia = i * angle
val x2 = center + (cos(ia) * (w - 2 * margin) / 2).toInt
val y2 = center - (sin(ia) * (w - 2 * margin) / 2).toInt
g.drawLine(center, center, x2, y2)
}
}
private def drawSpiral(g: Graphics2D): Unit = {
val (degrees: Double, center) = (toRadians(0.1), getWidth / 2)
val (a, b, c, end) = (0, 20, 1, 360 * 2 * 10 * degrees)
def plot(g: Graphics2D, x: Int, y: Int): Unit = g.drawOval(x, y, 1, 1)
def iter(theta: Double): Double = {
if (theta < end) {
val r = a + b * pow(theta, 1 / c)
val x = r * cos(theta)
val y = r * sin(theta)
plot(g, (center + x).toInt, (center - y).toInt)
iter(theta + degrees)
} else theta
}
g.setStroke(new BasicStroke(2))
g.setColor(Color.orange)
iter(0)
}
override def paintComponent(gg: Graphics): Unit = {
super.paintComponent(gg)
val g = gg.asInstanceOf[Graphics2D]
g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON)
drawGrid(g)
drawSpiral(g)
}
}
add(new ArchimedeanSpiral, BorderLayout.CENTER)
pack()
setDefaultCloseOperation(WindowConstants.EXIT_ON_CLOSE)
setLocationRelativeTo(null)
setResizable(false)
setVisible(true)
}
)
}
```
## Scilab
a = 3;
b = 2;
theta = linspace(0,10*%pi,1000);
r = a + b .* theta;
//1. Plot using polar coordinates
scf(1);
polarplot(theta,r);
//2. Plot using rectangular coordinates
//2.1 Convert coordinates using Euler's formula
z = r .* exp(%i .* theta);
x = real(z);
y = imag(z);
scf(2);
plot2d(x,y);
```
## Scheme
{{libheader|Scheme/PsTk}}
```scheme
(import (scheme base)
(scheme complex)
(rebottled pstk))
; settings for spiral
(define *resolution* 0.01)
(define *count* 2000)
(define *a* 10)
(define *b* 10)
(define *center*
(let ((size 200)) ; change this to alter size of display
(* size 1+i)))
(define (draw-spiral canvas)
(define (coords theta)
(let ((r (+ *a* (* *b* theta))))
(make-polar r theta)))
;
(do ((i 0 (+ i 1))) ; loop to draw spiral
((= i *count*) )
(let ((c (+ (coords (* i *resolution*)) *center*)))
(canvas 'create 'line
(real-part c) (imag-part c)
(+ 1 (real-part c)) (imag-part c)))))
(let ((tk (tk-start)))
(tk/wm 'title tk "Archimedean Spiral")
(let ((canvas (tk 'create-widget 'canvas)))
(tk/pack canvas)
(canvas 'configure
'height: (* 2 (real-part *center*))
'width: (* 2 (imag-part *center*)))
(draw-spiral canvas))
(tk-event-loop tk))
```
## Seed7
```seed7
$ include "seed7_05.s7i";
include "draw.s7i";
include "keybd.s7i";
const proc: main is func
local
const float: xCenter is 117.0;
const float: yCenter is 139.0;
const float: maxTheta is 10.0 * PI;
const float: delta is 0.01;
const float: a is 1.0;
const float: b is 7.0;
var float: theta is 0.0;
var float: radius is 0.0;
begin
screen(256, 256);
clear(curr_win, black);
KEYBOARD := GRAPH_KEYBOARD;
while theta <= maxTheta do
radius := a + b * theta;
point(round(xCenter + radius * cos(theta)),
round(yCenter - radius * sin(theta)), white);
theta +:= delta;
end while;
DRAW_FLUSH;
ignore(getc(KEYBOARD));
end func;
```
## Sidef
{{trans|Perl 6}}
```ruby
require('Imager')
define π = Num.pi
var (w, h) = (400, 400)
var img = %O.new(xsize => w, ysize => h)
for Θ in (0 .. 52*π -> by(0.025)) {
img.setpixel(
x => floor(cos(Θ / π)*Θ + w/2),
y => floor(sin(Θ / π)*Θ + h/2),
color => [255, 0, 0]
)
}
img.write(file => 'Archimedean_spiral.png')
```
Output image: [https://github.com/trizen/rc/blob/master/img/archimedean-spiral-sidef.png Archimedean spiral]
## Stata
```stata
clear all
scalar h=_pi/40
set obs 400
gen t=_n*h
gen x=(1+t)*cos(t)
gen y=(1+t)*sin(t)
line y x
```
## Tcl
This creates a little Tk GUI where you can interactively enter values for `a` and `b`. The spiral will be re-drawn automatically thanks to `trace`:
```Tcl
package require Tk
# create widgets
canvas .canvas
frame .controls
ttk::label .legend -text " r = a + b θ "
ttk::label .label_a -text "a ="
ttk::entry .entry_a -textvariable a
ttk::label .label_b -text "a ="
ttk::entry .entry_b -textvariable b
button .button -text "Redraw" -command draw
# layout
grid .canvas .controls -sticky nsew
grid .legend - -sticky ns -in .controls
grid .label_a .entry_a -sticky nsew -in .controls
grid .label_b .entry_b -sticky nsew -in .controls
grid .button - -sticky ns -in .controls
# make the canvas resize with the window
grid columnconfigure . 0 -weight 1
grid rowconfigure . 0 -weight 1
# spiral parameters:
set a .2
set b .05
proc draw {} {
variable a
variable b
# make sure inputs are valid:
if {![string is double $a] || ![string is double $b]} return
if {$a == 0 || $b == 0} return
set w [winfo width .canvas]
set h [winfo height .canvas]
set r 0
set pi [expr {4*atan(1)}]
set step [expr {$pi / $w}]
for {set t 0} {$r < 2} {set t [expr {$t + $step}]} {
set r [expr {$a + $b * $t}]
set y [expr {sin($t) * $r}]
set x [expr {cos($t) * $r}]
# transform to canvas co-ordinates
set y [expr {entier((1+$y)*$h/2)}]
set x [expr {entier((1+$x)*$w/2)}]
lappend coords $x $y
}
.canvas delete all
set id [.canvas create line $coords -fill red]
}
# draw whenever parameters are changed
# ";#" so extra trace arguments are ignored
trace add variable a write {draw;#}
trace add variable b write {draw;#}
wm protocol . WM_DELETE_WINDOW exit ;# exit when window is closed
update ;# lay out widgets before trying to draw
draw
vwait forever ;# go into event loop until window is closed
```
## VBA
```vb
Private Sub plot_coordinate_pairs(x As Variant, y As Variant)
Dim chrt As Chart
Set chrt = ActiveSheet.Shapes.AddChart.Chart
With chrt
.ChartType = xlXYScatter
.HasLegend = False
.SeriesCollection.NewSeries
.SeriesCollection.Item(1).XValues = x
.SeriesCollection.Item(1).Values = y
End With
End Sub
Public Sub main()
Dim x(1000) As Single, y(1000) As Single
a = 1
b = 9
For i = 0 To 1000
theta = i * WorksheetFunction.Pi() / 60
r = a + b * theta
x(i) = r * Cos(theta)
y(i) = r * Sin(theta)
Next i
plot_coordinate_pairs x, y
End Sub
```
## Yabasic
{{trans|Sinclair_ZX81_BASIC}}
```Yabasic
5 OPEN WINDOW 320, 200 : WINDOW ORIGIN "CC"
10 LET A=1.5
20 LET B=0.7
30 FOR T=0 TO 30*PI STEP 0.05
40 LET R=A+B*T
50 LINE TO R*COS(T),R*SIN(T)
60 NEXT T
```
## zkl
[[File:ArchimedeanSpiral.zk.jpg|250px|thumb|right]]
Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl
```zkl
fcn archimedeanSpiral(a,b,circles){
w,h:=640,640; centerX,centerY:=w/2,h/2;
bitmap:=PPM(w+1,h+1,0xFF|FF|FF); // White background
foreach deg in ([0.0 .. 360*circles]){
rad:=deg.toRad();
r:=rad*b + a;
x,y:=r.toRectangular(rad);
bitmap[centerX + x, centerY + y] = 0x00|FF|00; // Green dot
}
bitmap.writeJPGFile("archimedeanSpiral.jpg");
}(0,5,7);
```