Polyspiral
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.
The 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.
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
If animation is not practical in your programming environment, you may show a single frame instead.
J
<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
<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>
Lua
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
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.
<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.
<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
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>