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.
- 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
gnuplot
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>
- plotpoly.gp 1/10/17 aev
- Plotting a polyspiral and writing to the png-file.
- Note: assign variables: rng, d, clr, filename and ttl (before using load command).
- 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 versiong have pictures here on RC.
<lang gnuplot>
- PSpirals.gp 1/10/17 aev
- Plotting many polyspiral pictures.
- Note: assign variables: rng, d, clr, filename and ttl (before using load command).
- Direction d (-1 clockwise / 1 counter-clockwise)
- cd 'C:\gnupData'
- 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
- PS1 A polyspiral (Same size as PS0).
rng=10; d=1; clr = '"dark-green"'; filename = "PS1gp"; ttl = "Polyspiral #1 rng=10"; load "plotpoly.gp"
- PS3 A polyspiral
rng=20; d=-1; clr = '"red"'; filename = "PS3gp"; ttl = "Polyspiral #3 rng=20"; load "plotpoly.gp"
- PS4 A polyspiral having 4 secondary spirals.
rng=50; d=-1; clr = '"navy"'; filename = "PS4gp"; ttl = "Polyspiral #4 rng=50"; load "plotpoly.gp"
- 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"
- 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"
- ==============================
- NO PICTURES on RC starting from here, test it yourself
- ==============================
- PS2 A polyspiral
rng=20; d=1; clr = '"red"'; filename = "PS2gp"; ttl = "Polyspiral #2 rng=20"; load "plotpoly.gp"
- 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"
- PS8 Looks like PS4, but more distortion.
rng=150; d=-1; clr = '"green"'; filename = "PS8gp"; ttl = "Polyspiral #8 rng=150"; load "plotpoly.gp"
- PS9 Looks like PS2, but less loops..
rng=175; d=-1; clr = '"green"'; filename = "PS9gp"; ttl = "Polyspiral #9 rng=175"; load "plotpoly.gp"
- PS10 One loop of a spiral
rng=200; d=-1; clr = '"green"'; filename = "PS10gp"; ttl = "Polyspiral #10 rng=200"; load "plotpoly.gp"
- 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"
- 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"
- 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"
- 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"
- PS15 Not a polyspiral. Hmmm, just a star?
rng=90; d=-1; clr = '"navy"'; filename = "PS15gp"; ttl = "Polyspiral #15 rng=90"; load "plotpoly.gp"
- PS16 Not a polyspiral. Hmmm, just another star?
rng=300; d=-1; clr = '"navy"'; filename = "PS16gp"; ttl = "Polyspiral #16 rng=300"; load "plotpoly.gp"
- Continue plotting starting with a range rng=110 to 400+ step 10 to discover new figures.
- END ##
</lang>
- Output:
1. All PSpirals.gp file commands. 2. First 6 plotted png-files: PS0gp.png - PS6gp.
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>