Polyspiral: Difference between revisions

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A Polyspiral is a spiral made of multiple line segments, whereby each segment is larger (or smaller) than the previous one by a given amount. Each segment also changes direction at a given angle.

Task

Animate a series of polyspirals, by drawing a complete spiral then incrementing the angle, and (after clearing the background) drawing the next, and so on. Every spiral will be a frame of the animation. The animation may stop as it goes full circle or continue indefinitely. The given input values may be varied.

If animation is not practical in your programming environment, you may show a single frame instead.

Pseudo code

    set incr to 0.0

    // animation loop
    WHILE true 

        incr = (incr + 0.05) MOD 360
        x = width / 2
        y = height / 2
        length = 5
        angle = incr

        // spiral loop
        FOR 1 TO 150
            drawline
            change direction by angle
            length = length + 3
            angle = (angle + incr) MOD 360
        ENDFOR

C++

This Windows programm has no animation, it will simply save 100 bitmaps onto your harddrive <lang cpp>

include <windows.h>
include <sstream>
include <ctime>

const float PI = 3.1415926536f, TWO_PI = 2.f * PI; class vector2 { public:

   vector2( float a = 0, float b = 0 ) { set( a, b ); }
   void set( float a, float b ) { x = a; y = b; }
   void rotate( float r ) {
       float _x = x, _y = y,
              s = sinf( r ), c = cosf( r ),
              a = _x * c - _y * s, b = _x * s + _y * c;
       x = a; y = b;
   }
   vector2 add( const vector2& v ) {
       x += v.x; y += v.y;
       return *this;
   }
   float x, y;

}; 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;

}; int main( int argc, char* argv[] ) {

   srand( unsigned( time( 0 ) ) );
   myBitmap bmp;
   bmp.create( 600, 600 ); bmp.clear();
   HDC dc = bmp.getDC();
   float fs = ( TWO_PI ) / 100.f;
   int index = 0;
   std::string a = "f://users//images//test", b;
   float ang, len;
   vector2 p1, p2;

   for( float step = 0.1f; step < 5.1f; step += .05f ) {
       ang = 0; len = 2;
       p1.set( 300, 300 );
       bmp.setPenColor( RGB( rand() % 50 + 200, rand() % 300 + 220, rand() % 50 + 200 ) );
       for( float xx = 0; xx < TWO_PI; xx += fs ) {
           MoveToEx( dc, (int)p1.x, (int)p1.y, NULL );
           p2.set( 0, len ); p2.rotate( ang ); p2.add( p1 );
           LineTo( dc, (int)p2.x, (int)p2.y );
           p1 = p2; ang += step; len += step;
       }
       std::ostringstream ss; ss << index++;
       b = a + ss.str() + ".bmp";
       bmp.saveBitmap( b );
       bmp.clear();
   }
   return 0;

} </lang>

Gnuplot

Works with: gnuplot version 5.0 (patchlevel 3) and above

Plotting a polyspiral file-function for the load command

plotpoly.gp file for the load command is the only possible imitation of the fine function in the gnuplot. <lang gnuplot>

1. plotpoly.gp 1/10/17 aev
2. Plotting a polyspiral and writing to the png-file.
3. Note: assign variables: rng, d, clr, filename and ttl (before using load command).
4. Direction d (-1 clockwise / 1 counter-clockwise)

reset set terminal png font arial 12 size 640,640 ofn=filename.".png" set output ofn unset border; unset xtics; unset ytics; unset key; set title ttl font "Arial:Bold,12" set parametric c=rng*pi; set xrange[-c:c]; set yrange[-c:c]; set dummy t plot [0:c] t*cos(d*t), t*sin(d*t) lt rgb @clr set output </lang>

Plotting many versions of a polyspiral.

Note: only 6 versions have pictures here on RC.

Output PS0gp.png

Output PS1gp.png

Output PS3gp.png

Output PS4gp.png

Output PS5gp.png

Output PS6gp.png

1. PSpirals.gp 1/10/17 aev
2. Plotting many polyspiral pictures.
3. Note: assign variables: rng, d, clr, filename and ttl (before using load command).
4. Direction d (-1 clockwise / 1 counter-clockwise)
cd 'C:\gnupData'

1. PS0 smooth spiral (not a polyspiral)

reset set terminal png font arial 12 size 640,640 set output "PS0gp.png" set title "Smooth spiral #0 rng=10" font "Arial:Bold,12" set parametric c=10*pi; set trange [0:c]; set xrange[-c:c]; set yrange[-c:c]; set samples 1000 plot t*cos(t), t*sin(t) lt rgb "red" set output

1. PS1 A polyspiral (Same size as PS0).

rng=10; d=1; clr = '"dark-green"'; filename = "PS1gp"; ttl = "Polyspiral #1 rng=10"; load "plotpoly.gp"

1. PS3 A polyspiral

rng=20; d=-1; clr = '"red"'; filename = "PS3gp"; ttl = "Polyspiral #3 rng=20"; load "plotpoly.gp"

1. PS4 A polyspiral having 4 secondary spirals.

rng=50; d=-1; clr = '"navy"'; filename = "PS4gp"; ttl = "Polyspiral #4 rng=50"; load "plotpoly.gp"

1. PS5 Not a polyspiral, but has 8 secondary spirals.

rng=75; d=-1; clr = '"navy"'; filename = "PS5gp"; ttl = "Polyspiral #5 rng=75"; load "plotpoly.gp"

1. PS6 Not a polyspiral, just a nice figure (seen in zkl).

rng=100; d=-1; clr = '"navy"'; filename = "PS6gp"; ttl = "Polyspiral #6 rng=100"; load "plotpoly.gp"

1. ==============================
  1. 1. NO PICTURES on RC starting from here, test it yourself

1. PS2 A polyspiral

rng=20; d=1; clr = '"red"'; filename = "PS2gp"; ttl = "Polyspiral #2 rng=20"; load "plotpoly.gp"

1. PS7 Looks like PS5, but has 5 secondary spirals (not 8)

rng=120; d=-1; clr = '"green"'; filename = "PS7gp"; ttl = "Polyspiral #7 rng=120"; load "plotpoly.gp"

1. PS8 Looks like PS4, but more distortion.

rng=150; d=-1; clr = '"green"'; filename = "PS8gp"; ttl = "Polyspiral #8 rng=150"; load "plotpoly.gp"

1. PS9 Looks like PS2, but less loops..

rng=175; d=-1; clr = '"green"'; filename = "PS9gp"; ttl = "Polyspiral #9 rng=175"; load "plotpoly.gp"

1. PS10 One loop of a spiral

rng=200; d=-1; clr = '"green"'; filename = "PS10gp"; ttl = "Polyspiral #10 rng=200"; load "plotpoly.gp"

1. PS11 Polyspiral with line segments crossing other line segments.

rng=30; d=-1; clr = '"navy"'; filename = "PS11gp"; ttl = "Polyspiral #11 rng=30"; load "plotpoly.gp"

1. PS12 Looks like PS4, but has 5 secondary spirals.

rng=40; d=-1; clr = '"navy"'; filename = "PS12gp"; ttl = "Polyspiral #12 rng=40"; load "plotpoly.gp"

1. PS13 Looks like PS5, but has 8 secondary spirals.

rng=60; d=-1; clr = '"navy"'; filename = "PS13gp"; ttl = "Polyspiral #13 rng=60"; load "plotpoly.gp"

1. PS14 Looks like PS4, but has 5 secondary spirals.

rng=80; d=-1; clr = '"navy"' filename = "PS14gp"; ttl = "Polyspiral #14 rng=80"; load "plotpoly.gp"

1. PS15 Not a polyspiral. Hmmm, just a star?

rng=90; d=-1; clr = '"navy"'; filename = "PS15gp"; ttl = "Polyspiral #15 rng=90"; load "plotpoly.gp"

1. PS16 Not a polyspiral. Hmmm, just another star?

rng=300; d=-1; clr = '"navy"'; filename = "PS16gp"; ttl = "Polyspiral #16 rng=300"; load "plotpoly.gp"

1. Continue plotting starting with a range rng=110 to 400+ step 10 to discover new figures.
2. END ##

</lang>

Output:

1. All PSpirals.gp file commands.
2. First 6 plotted png-files: PS0gp.png - PS6gp.

Plotting a polyspiral file-function for the load command (for animation)

plotpolya.gp file for the load command is the only possible imitation of the fine function in the gnuplot. <lang gnuplot>

1. plotpolya.gp 1/19/17 aev
2. Plotting a polyspiral and writing to the png-file. Simple plot for animation.
3. Note: assign variables: rng, d, clr, filename (before using load command).
4. ==== NO ttl (title) in this version.

reset set terminal png font arial 12 size 640,640 ofn=filename.".png" set output ofn unset border; unset xtics; unset ytics; unset key; set parametric c=rng*pi; set xrange[-c:c]; set yrange[-c:c]; set dummy t plot [0:c] t*cos(d*t), t*sin(d*t) lt rgb @clr set output </lang>

Plotting many polyspiral and other pictures for animation.

Note: No generated pictures here on RC. <lang gnuplot>

1. PSpirals4a.gp 1/19/17 aev
2. Plotting many polyspiral and other pictures for animation
3. Notes: 1. Assign variables: rng, d, clr, filename(before using load command).
4. ====== 2. NO title in this version.
5. 3. Primarily range is changed.
6. Direction d (-1 clockwise / 1 counter-clockwise)
cd 'C:\gnupData'

1. ====== for PolySpirsAnim.gif ==========================================
2. PS0 A polyspiral (direction: counter-clockwise).

rng=10; d=1; clr = '"red"'; filename = "PS0"; load "plotpolya.gp";

1. PS1 A polyspiral (direction: clockwise).

rng=20; d=-1; clr = '"red"'; filename = "PS1"; load "plotpolya.gp";

1. PS2 A polyspiral. Looks like PS1, but less loops..

rng=175; d=-1; clr = '"red"'; filename = "PS2"; load "plotpolya.gp";

1. PS3 Polyspiral with line segments crossing other line segments.

rng=30; d=-1; clr = '"red"'; filename = "PS3"; load "plotpolya.gp";

1. PS4 A polyspiral having 4 secondary spirals.

rng=50; d=-1; clr = '"red"'; filename = "PS4"; load "plotpolya.gp";

1. PS5 A polyspiral. Looks like PS4, but has 5 secondary spirals.

rng=40; d=-1; clr = '"red"'; filename = "PS5"; load "plotpolya.gp";

1. PS6 A polyspiral. Looks like PS4, but has more distortion.

rng=150; d=-1; clr = '"red"'; filename = "PS6"; load "plotpolya.gp";

1. PS7 A polyspiral. Has 8 secondary spirals and even more distortion.

rng=60; d=-1; clr = '"red"'; filename = "PS7"; load "plotpolya.gp";

1. ====== for NiceFigsAnim.gif ==========================================
2. PS8 Not a polyspiral, but has 8 secondary spirals.

rng=75; d=-1; clr = '"navy"'; filename = "PS8"; load "plotpolya.gp";

1. PS9 Looks like PS8, but has 5 secondary spirals.

rng=80; d=-1; clr = '"navy"'; filename = "PS9"; load "plotpolya.gp";

1. PS10 Looks like PS8, but has 5 secondary spirals (not 8)

rng=120; d=-1; clr = '"navy"'; filename = "PS10"; load "plotpolya.gp";

1. PS11 Not a polyspiral, just nice figure.

rng=100; d=-1; clr = '"navy"'; filename = "PS11"; load "plotpolya.gp";

1. PS12 Not a polyspiral. Hmmm, just a star?

rng=90; d=-1; clr = '"navy"'; filename = "PS12"; load "plotpolya.gp";

1. PS13 Not a polyspiral. Hmmm, just another star?

rng=300; d=-1; clr = '"navy"'; filename = "PS13"; load "plotpolya.gp";

1. PS14 Not a polyspiral, but has many short secondary spirals.

rng=700; d=-1; clr = '"navy"'; filename = "PS14"; load "plotpolya.gp"; </lang>

Output:

1. All PSpirals4a.gp file commands.
2. 15 plotted png-files: PS0.png - PS14.png.

Creating 2 animated gif-files.

Note: No gif-files. File upload still not allowed. So, test it yourself.

File:PolySpirsAnim.gif

Output PolySpirsAnim.gif

File:NiceFigsAnim.gif

Output NiceFigsAnim.gif

1. Animation for polyspirals PS0 - PS6

reset set terminal gif animate delay 100 loop 2 size 640,640 set output 'PolySpirsAnim.gif' unset border; unset xtics; unset ytics; unset key; unset autoscale set xrange[0:640] set yrange[0:640] do for [i=0:6]{plot 'PS'.i.'.png' binary filetype=png with rgbimage} set output

1. Animation for nice figures PS8 - PS14

reset set terminal gif animate delay 100 loop 2 size 640,640 set output 'NiceFigsAnim.gif' unset border; unset xtics; unset ytics; unset key; unset autoscale set xrange[0:640] set yrange[0:640] do for [i=8:14]{plot 'PS'.i.'.png' binary filetype=png with rgbimage} set output </lang>

Output:

2 created gif-files: PolySpirsAnim.gif and NiceFigsAnim.gif

Showing 2 animated gif-files.

Create 2 the following html-files and envoke them in browser. <lang html> <html><body>

Gnuplot: Polyspirals animation >> <a href="NiceFigsAnim.html">Next: Nice figures animation</a>

 <img src="PolySpirsAnim.gif">

</body></html> </lang> <lang html> <html><body>

Gnuplot: Nice figures animation >> <a href="PolySpirsAnim.html">Next: Polyspirals animation</a>

 <img src="NiceFigsAnim.gif">

</body></html> </lang>

Output:

2 pages with animation.

J

Translation of: java

<lang J>require 'gl2 trig media/imagekit' coinsert 'jgl2'

DT =: %30 NB. seconds ANGLE =: 0.025p1 NB. radians DIRECTION=: 0 NB. radians

POLY=: noun define

 pc poly;pn "Poly Spiral";
 minwh 320 320; cc isi isigraph;

)

poly_run=: verb define

 wd POLY,'pshow'
 wd 'timer ',":DT * 1000

)

poly_close=: verb define

 wd 'timer 0; pclose'

)

sys_timer_z_=: verb define

 recalcAngle_base_ 
 wd 'psel poly; set isi invalid'

)

poly_isi_paint=: verb define

 drawPolyspiral DIRECTION

)

recalcAngle=: verb define

 DIRECTION=: 2p1 | DIRECTION + ANGLE

)

drawPolyspiral=: verb define

 glclear
 x1y1 =. (glqwh)%2
 a=. -DIRECTION
 len=. 5
 for_i. i.150 do.
   glpen glrgb Hue a % 2p1
   x2y2=. x1y1 + len*(cos,sin) a
   gllines <.x1y1,x2y2
   x1y1=. x2y2
   len=. len+3
   a=. 2p1 | a - DIRECTION
 end.

)

poly_run</lang>

Note that we're using a lot of wd commands here. You'll need to be running jqt for this to work.

Java

Works with: Java version 8

<lang java>import java.awt.*; import java.awt.event.ActionEvent; import javax.swing.*;

public class PolySpiral extends JPanel {

   double inc = 0;

   public PolySpiral() {
       setPreferredSize(new Dimension(640, 640));
       setBackground(Color.white);

       new Timer(40, (ActionEvent e) -> {
           inc = (inc + 0.05) % 360;
           repaint();
       }).start();
   }

   void drawSpiral(Graphics2D g, int len, double angleIncrement) {

       double x1 = getWidth() / 2;
       double y1 = getHeight() / 2;
       double angle = angleIncrement;

       for (int i = 0; i < 150; i++) {

           g.setColor(Color.getHSBColor(i / 150f, 1.0f, 1.0f));

           double x2 = x1 + Math.cos(angle) * len;
           double y2 = y1 - Math.sin(angle) * len;
           g.drawLine((int) x1, (int) y1, (int) x2, (int) y2);
           x1 = x2;
           y1 = y2;

           len += 3;

           angle = (angle + angleIncrement) % (Math.PI * 2);
       }
   }

   @Override
   public void paintComponent(Graphics gg) {
       super.paintComponent(gg);
       Graphics2D g = (Graphics2D) gg;
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING,
               RenderingHints.VALUE_ANTIALIAS_ON);

       drawSpiral(g, 5, Math.toRadians(inc));
   }

   public static void main(String[] args) {
       SwingUtilities.invokeLater(() -> {
           JFrame f = new JFrame();
           f.setDefaultCloseOperation(JFrame.EXIT_ON_CLOSE);
           f.setTitle("PolySpiral");
           f.setResizable(true);
           f.add(new PolySpiral(), BorderLayout.CENTER);
           f.pack();
           f.setLocationRelativeTo(null);
           f.setVisible(true);
       });
   }

}</lang>

Kotlin

Translation of: Java

<lang scala>// version 1.1.0

import java.awt.* import java.awt.event.ActionEvent import javax.swing.*

class PolySpiral() : JPanel() {

   private var inc = 0.0

   init {
       preferredSize = Dimension(640, 640)
       background = Color.white
       Timer(40) {
           inc = (inc + 0.05) % 360.0
           repaint()
       }.start()
   }

   private fun drawSpiral(g: Graphics2D, length: Int, angleIncrement: Double) {
       var x1 = width / 2.0
       var y1 = height / 2.0
       var len = length
       var angle = angleIncrement       
       for (i in 0 until 150) {
           g.setColor(Color.getHSBColor(i / 150f, 1.0f, 1.0f))
           val x2 = x1 + Math.cos(angle) * len
           val y2 = y1 - Math.sin(angle) * len
           g.drawLine(x1.toInt(), y1.toInt(), x2.toInt(), y2.toInt())
           x1 = x2
           y1 = y2
           len += 3
           angle = (angle + angleIncrement) % (Math.PI * 2.0)
       }
   }

   override protected fun paintComponent(gg: Graphics) {
       super.paintComponent(gg)
       val g = gg as Graphics2D
       g.setRenderingHint(RenderingHints.KEY_ANTIALIASING, RenderingHints.VALUE_ANTIALIAS_ON) 
       drawSpiral(g, 5, Math.toRadians(inc))
   }

}

fun main(args: Array<String>) {

   SwingUtilities.invokeLater {
       val f = JFrame()
       f.defaultCloseOperation = JFrame.EXIT_ON_CLOSE
       f.title = "PolySpiral"
       f.setResizable(true)
       f.add(PolySpiral(), BorderLayout.CENTER)
       f.pack()
       f.setLocationRelativeTo(null)
       f.setVisible(true)
   }

}</lang>

Lua

Library: LÖVE

LÖVE defaults to animating at sixty frames per second, so the patterns become very complex very quickly. <lang Lua>function love.load ()

   love.window.setTitle("Polyspiral")
   incr = 0

end

function love.update (dt)

   incr = (incr + 0.05) % 360
   x1 = love.graphics.getWidth() / 2
   y1 = love.graphics.getHeight() / 2
   length = 5
   angle = incr

end

function love.draw ()

   for i = 1, 150 do
       x2 = x1 + math.cos(angle) * length
       y2 = y1 + math.sin(angle) * length
       love.graphics.line(x1, y1, x2, y2)
       x1, y1 = x2, y2
       length = length + 3
       angle = (angle + incr) % 360
   end

end</lang>

PARI/GP

Works with: PARI/GP version 2.7.4 and above

Plotting helper functions

Both versions #1 and #2 are based on using my own small plotting helper functions. You can find a few others on OEIS Wiki and here on RC Wiki.

<lang parigp> \\ Plot the line from x1,y1 to x2,y2. plotline(x1,y1,x2,y2,w=0)={plotmove(w, x1,y1);plotrline(w,x2-x1,y2-y1);} \\ Convert degrees to radians. rad2(degs)={return(degs*Pi/180.0)} \\ Convert Polar coordinates to Cartesian. cartes2(r,a,rndf=0)={my(v,x,y); x=r*cos(a); y=r*sin(a);

 if(rndf==0, return([x,y]), return(round([x,y])))}

</lang>

Version #1. Polyspiral (a spiral made of multiple line segments).

In this version function plotpspiral() was translated from Java and J. Some tweaks and options were added to make it reusable and outputting differently looking polyspirals. There are no animation features in PARI/GP.

Output Polyspiral1.png

Output Polyspiral2.png

Output Polyspiral3.png

Output Polyspiral3b.png

Output Polyspiral4.png

<lang parigp> \\Polyspiral (a spiral made of multiple line segments) \\ 4/15/16 aev plotpspiral(size,lim,ai,d,di,c)={ my(x1,y1,x2,y2,air=ai*Pi,a,sai=Strprintf("%.3f",ai)); print(" *** Polyspiral, size=",size," lim=",lim," ai=",sai," d=",d," di=",di); x1=0; y1=0; a=air; for(i=0, lim,

   if(c==0, x2=x1+cos(a)*d; y2=y1-sin(a)*d,
            x2=x1-sin(a)*d; y2=y1+cos(a)*d;);
   plotline(x1,y1,x2,y2);
   x1=x2; y1=y2; d+=di; a+=air;
  );\\fend i

}

\\ Polyspiral() - Where: ai is an angle increment (in radians), d is a distance/length, \\ c is a direction 0/1 (clockwise/counter-clockwise); other parameters are self explanative. \\ 4/15/16 aev Last updated: 4/18/16 polyspiral(size,lim,ai,d,di,c=0)={ plotinit(0); plotcolor(0,3); \\blue plotscale(0, -size,size, -size,size); plotmove(0, 0,0); plotpspiral(size,lim,ai,d,di,c); plotdraw([0,size,size]); }

{\\ Executing: polyspiral(1500,1500,0.25,9,5); \\Polyspiral1.png polyspiral(1500,1500,0.25,3,2); \\Polyspiral2.png polyspiral(10000,10000,0.03,3,2); \\Polyspiral3.png polyspiral(10000,10000,0.03,3,2,1); \\Polyspiral3b.png polyspiral(100000,100000,0.03,3,2);\\Polyspiral4.png } </lang>

Output:


> polyspiral(1500,1500,0.25,9,5);  \\Polyspiral1.png
*** Polyspiral, size=1500 lim=1500 ai=0.250 d=9 di=5
 
> polyspiral(1500,1500,0.25,3,2);  \\Polyspiral2.png
*** Polyspiral, size=1500 lim=1500 ai=0.250 d=3 di=2
 
> polyspiral(10000,10000,0.03,3,2);  \\Polyspiral3.png
*** Polyspiral, size=100000 lim=100000 ai=0.030 d=3 di=2

> polyspiral(10000,10000,0.03,3,2,1);  \\Polyspiral3b.png
*** Polyspiral, size=100000 lim=100000 ai=0.030 d=3 di=2

> polyspiral(100000,100000,0.03,3,2);  \\Polyspiral4.png
*** Polyspiral, size=100000 lim=100000 ai=0.030 d=3 di=2

Version #2. Multi-spiral figure translated from zkl.

This is definitely not a polyspiral, but a very nice "multi-spiral" figure similar to shown in zkl and in a few other languages. Also, there is a very nice and impressive animation created in zkl, but not possible in PARI/GP.

Translation of: zkl

Output Spiralz.png

<lang parigp> \\ plotpspiralz() Multi-spiral figure translated from zkl using my own ploting functions. \\ 4/15/16 aev plotpspiralz(size,lim,ai,di,lim2)={ my(x1,y1,u1,v1,air=rad2(ai),a,sai=Strprintf("%.3f",ai),sdi=Strprintf("%.3f",di),

  sz2=size\2,aj,inc,ao,x,y,u,v,vc,r2i=rad2(130.0),d=0.0);

print(" *** Spiralz: size=",size," lim=",lim," ai=",sai," di=",sdi," lim2=",lim2); x1=0; y1=0; u1=0; v1=0; for(i=1, lim,

 r=0.0; a=0.0;ao=0.0;
 if(i>1, inc=air+r2i, inc=air);
 for(j=1, lim2,
   d=r+di; aj=a+inc;
   vc=cartes2(r,a); x=vc[1]; y=vc[2];
   vc=cartes2(r,aj); u=vc[1]; v=vc[2];
   plotline(ao+x,ao+y,ao+u,ao+v);
   r=d; a=aj;
 );\\fend j
 air+=0.05;

);\\fend i }

\\ Spiralz() - Where: ai is an angle increment (in radians), di is a distance/length \\ increment, other parameters are self explanative. \\ 4/15/16 aev Spiralz(size,lim,ai,di,lim2)={ plotinit(0); plotcolor(0,3); \\blue plotscale(0, -size,size, -size,size); \\plotscale(0, 0,size, 0,size); plotmove(0, 0,0); plotpspiralz(size,lim,ai,di,lim2); plotdraw([0,size,size]); }

{\\ Executing: Spiralz(640,2,3.0,3.0,128); \\Spiralz1.png } </lang>

Output:

> Spiralz(640,2,3.0,3.0,128);  \\Spiralz1.png
 *** Spiralz: size=640 lim=2 ai=3.000 di=3.000 lim2=128

Phix

Space toggles the timer, '+' increases speed (up to 100 FPS), '-' decreases speed. 'M' toggles "mod360", which inverts the angle every 360/2PI or so, producing non-true polyspirals, but quite interesting nevertheless. <lang Phix>-- -- demo\rosetta\Polyspiral.exw -- =========================== -- include ..\pGUI\pGUI.e

Ihandle dlg, canvas, timer cdCanvas cddbuffer, cdcanvas

constant TITLE = "Polyspiral"

atom incr = 0 bool mod360 = false

procedure Polyspiral(atom x1, y1) atom angle = incr integer len = 5

   incr += 0.05
   if mod360 then
       incr = mod(incr,360)
   end if
   for i=1 to 150 do
       atom x2 = x1 + cos(angle)*len
       atom y2 = y1 + sin(angle)*len
       cdCanvasSetForeground(cddbuffer, i*#200+i*#40+i*#10)
       cdCanvasLine(cddbuffer, x1, y1, x2, y2)
       {x1, y1} = {x2, y2}
       len += 3
       angle += incr
       if mod360 then
           angle = mod(angle,360)
       end if
   end for

end procedure

function redraw_cb(Ihandle /*ih*/, integer /*posx*/, integer /*posy*/)

   integer {w, h} = IupGetIntInt(canvas, "DRAWSIZE")
   cdCanvasActivate(cddbuffer)
   cdCanvasClear(cddbuffer)
   Polyspiral(w/2, h/2)
   cdCanvasFlush(cddbuffer)
   integer ms = IupGetInt(timer,"TIME")
   IupSetStrAttribute(dlg, "TITLE", "%s (timer=%d [%g FPS], angle %3.2f%s)",
                      {TITLE,ms,1000/ms,incr,iff(mod360?" (mod360)":"")})
   return IUP_DEFAULT

end function

function timer_cb(Ihandle /*ih*/)

   IupUpdate(canvas)
   return IUP_IGNORE

end function

function map_cb(Ihandle ih)

   cdcanvas = cdCreateCanvas(CD_IUP, ih)
   cddbuffer = cdCreateCanvas(CD_DBUFFER, cdcanvas)
   cdCanvasSetBackground(cddbuffer, CD_WHITE)
   cdCanvasSetForeground(cddbuffer, CD_GRAY)
   return IUP_DEFAULT

end function

function esc_close(Ihandle /*ih*/, atom c)

   if c=K_ESC then return IUP_CLOSE end if
   if c=' ' then
       IupSetInt(timer,"RUN",not IupGetInt(timer,"RUN"))
   elsif find(c,"+-") then
       -- ('+' increases speed, by decreasing TIME)
       IupSetInt(timer,"TIME",max(10,IupGetInt(timer,"TIME")-(','-c)*10))
       IupSetInt(timer,"RUN",0)
       IupSetInt(timer,"RUN",1)
   elsif upper(c)='M' then
       mod360 = not mod360
   end if
   return IUP_CONTINUE

end function

procedure main()

   IupOpen(join_path({"..","pGUI"},1))

   canvas = IupCanvas(NULL)
   IupSetAttribute(canvas, "RASTERSIZE", "640x640")
   IupSetCallback(canvas, "MAP_CB", Icallback("map_cb"))
   IupSetCallback(canvas, "ACTION", Icallback("redraw_cb"))

   timer = IupTimer(Icallback("timer_cb"), 20)

   dlg = IupDialog(canvas)
   IupSetAttribute(dlg, "TITLE", TITLE)
   IupSetCallback(dlg, "K_ANY", Icallback("esc_close"))

   IupShow(dlg)
   IupSetAttribute(canvas, "RASTERSIZE", NULL)
   IupMainLoop()
   IupClose()

end procedure

main()</lang>

zkl

If you click on the image, it is animated.

Uses the PPM class from http://rosettacode.org/wiki/Bitmap/Bresenham%27s_line_algorithm#zkl <lang zkl>w,h:=640,640; bitmap:=PPM(w,h,0xFF|FF|FF); // White background angleIncrement:=(3.0).toRad(); while(True){

  r,angle:=0.0, 0.0;
  ao,len,inc:=w/2, 2.5, angleIncrement+(130.0).toRad();
  foreach c in (128){
     s,a:=r + len, angle + inc;
     x,y:=r.toRectangular(angle);
     u,v:=r.toRectangular(a);
     c=c.shiftLeft(21) + c.shiftLeft(10) + c*8;  // convert c to a RGB
     bitmap.line(ao+x,ao+y, ao+u,ao+v, c);
     r,angle=s,a;
  }
  bitmap.writeJPGFile("polyspiral.zkl.jpg");
  bitmap.fill(0xFF|FF|FF);  // White background
  angleIncrement=(angleIncrement + 0.05);
  Atomic.sleep(3);

}</lang>