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Your job is to animate this circle illusion. It looks like the points rotating inside of the circle, but they are actually just moving in straight lines.

enter image description here


  • The result has to be animated. The way you do the animation is irrelevant, it can generate a .gif, it can draw to a window, some device screen or whatever.
  • This is a popularity contest, so you might want to add some additional features to your program to get more upvotes, for example varying the number of points.
  • The winner is the most upvoted valid answer 7 days after the last valid submission.
  • The answers that will actually implement points moving on straight lines and not another way around are more welcomed
share|improve this question
"winner is the most upvoted valid after 7 days". So if someone posts something every 6 days until the stars die, we have no winner? –  Kevin L Jul 21 '14 at 19:52
@KevinL that is unlikely to happen and I don't think those 15 extra rep are that important compared to all the upvotes you'd get from this question being bumped to the top every 6 days. –  Martin Büttner Jul 21 '14 at 20:09
Sometimes I wonder if some people do these just to get a job done... –  Daniel Pendergast Jul 23 '14 at 19:50
"It looks like the points rotating inside of the circle, but they are actually just moving in straight lines.", or, maybe they are really rotating inside a circle and appear to move in straight lines ... –  coredump Jul 26 '14 at 21:13
Can't.. get this animation.. out of my mind.. especially the 3-point version! –  Thomas Jul 28 '14 at 12:32

11 Answers 11

up vote 96 down vote accepted

Python 3.4

Using the turtle module. The turtles are different colours and they always face in the same direction, so they can be easily seen to be moving along straight lines by just focusing on one of them. Despite this the circle illusion is still strong.

11 turtles

The illusion still seems quite strong even with just 3 or 4 turtles:

3 turtles4 turtles

The framerate is reduced considerably for all of these GIF examples, but it doesn't seem to detract from the illusion. Running the code locally gives a smoother animation.

import turtle
import time
from math import sin, pi
from random import random

def circle_dance(population=11, resolution=480, loops=1, flip=0, lines=0):
    population = int(population)
    resolution = int(resolution)
    radius = 250
    screen = turtle.Screen()
    if lines:
        arrange_lines(population, radius)
    turtles = [turtle.Turtle() for i in range(population)]
    for i in range(population):
        dancer = turtles[i]
        make_dancer(dancer, i, population)
    animate(turtles, resolution, screen, loops, flip, radius)

def arrange_lines(population, radius):
    artist = turtle.Turtle()
    for n in range(population):
        artist.setposition(0, 0)
        artist.setheading(n / population * 180)
        artist.forward(radius * 2)

def make_dancer(dancer, i, population):
    dancer.setheading(i / population * 180)

def random_turtle_colour():
    return random() * 0.9, 0.5 + random() * 0.5, random() * 0.7

def animate(turtles, resolution, screen, loops, flip, radius):
    delay = 4 / resolution      # 4 seconds per repetition
    while True:
        for step in range(resolution):
            timer = time.perf_counter()
            phase = step / resolution * 2 * pi
            draw_dancers(turtles, phase, screen, loops, flip, radius)
            elapsed = time.perf_counter() - timer
            adjusted_delay = max(0, delay - elapsed)

def draw_dancers(turtles, phase, screen, loops, flip, radius):
    population = len(turtles)
    for i in range(population):
        individual_phase = (phase + i / population * loops * pi) % (2*pi)
        dancer = turtles[i]
        if flip:
            if pi / 2 < individual_phase <= 3 * pi / 2:
        distance = radius * sin(individual_phase)
        dancer.setposition(0, 0)

if __name__ == '__main__':
    import sys
    circle_dance(*(float(n) for n in sys.argv[1:]))

For contrast here are some that really do rotate:

23 loop turtles23 trefoil turtles

...or do they?

The code can be run with 5 optional arguments: population, resolution, loops, flip and lines.

  • population is the number of turtles
  • resolution is the time resolution (number of animation frames per repetition)
  • loops determines how many times the turtles loop back on themselves. The default of 1 gives a standard circle, other odd numbers give that number of loops in the string of turtles, while even numbers give a string of turtles disconnected at the ends, but still with the illusion of curved motion.
  • flip if non-zero causes the turtles to flip direction for their return trip (as suggested by aslum so that they are never moving backwards). As default they keep a fixed direction to avoid the visual distraction at the endpoints.
  • lines if non-zero displays the lines on which the turtles move, for consistency with the example image in the question.

Examples with flip set, with and without lines. I've left my main example above without flip as I prefer not to have the sporadic jump, but the edge of the circle does look smoother with all the turtles aligned, so the option is there for people to choose whichever style they prefer when running the code.

11 turtles with flip and lines11 turtles with flip

It might not be immediately obvious how the images above were all produced from this same code. In particular the image further up which has a slow outer loop and a fast inner loop (the one that looks like a cardioid that someone accidentally dropped). I've hidden the explanation of this one below in case anyone wants to delay finding out while experimenting/thinking.

The animation with an inner and outer loop of different sizes was created by setting the number of loops to 15 and leaving the number of turtles at 23 (too low to represent 15 loops). Using a large number of turtles would result in 15 clearly defined loops. Using too few turtles results in aliasing (for the same reason as in image processing and rendering). Trying to represent too high a frequency results in a lower frequency being displayed, with distortion.

Trying out different numbers I found some of these distortions more interesting than the more symmetrical originals, so I wanted to include one here...

share|improve this answer
I like turtles. –  FreeAsInBeer Jul 23 '14 at 13:16
I shelled out +1 for the turtles –  MrEngineer13 Jul 23 '14 at 13:25
You're welcome! –  ProgramFOX Jul 23 '14 at 14:00
@aslum that would be a straightforward change to make, but I wanted their orientation frozen to really emphasise that they do not deviate from their straight line course. Maybe I should add it to the code as an option so people can choose the approach they prefer. –  trichoplax Jul 23 '14 at 19:13
+1 - It'd be awesome to see a marching band do some of these funkier ones! –  mkoistinen Jul 25 '14 at 20:10



enter image description here

#include <stdio.h>
#include <Windows.h>
#include <Math.h>

int round (double r) { return (r > 0.0) ? (r + 0.5) : (r - 0.5); }
void print (int x, int y, char c) {
    COORD p = { x, y };
    SetConsoleCursorPosition(GetStdHandle(STD_OUTPUT_HANDLE), p);
    printf("%c", c);

int main ()
    float pi = 3.14159265358979323846;
    float circle = pi * 2;
    int len = 12;
    int hlen = len / 2;
    int cx = 13;
    int cy = 8;
    float w = 11.0;
    float h =  8.0;
    float step = 0.0;

    while (1)
        system("cls"); // xD

        for (int i = 0; i < len; i++)
            float a = (i / (float)len) * circle;
            int x = cx + round(cos(a) * w);
            int y = cy + round(sin(a) * h);
            print(x, y, 'O');

            if (i < hlen) continue;

            step -= 0.05;
            float range = cos(a + step);
            x = cx + round(cos(a) * (w - 1) * range);
            y = cy + round(sin(a) * (h - 1) * range);
            print(x, y, 'O');


    return 0;
share|improve this answer
In some frames it's a bit off. But congrats for doing it in ASCII! –  justhalf Jul 22 '14 at 10:05
+1 for ASCII and system("cls"); // xD –  HackerCow Jul 22 '14 at 10:49
This is beautiful. –  trichoplax Jul 23 '14 at 9:46
This one works on linux. (although quite miserably) –  user824294 Jul 23 '14 at 10:26
Obligatory hater comment: "This isn't C! The standard doesn't define Sleep, COORD or SetConsoleCursorPosition!" –  immibis Jul 27 '14 at 21:13

SVG (no Javascript)

JSFiddle link here

<?xml version="1.0"?>
<svg xmlns="http://www.w3.org/2000/svg" xmlns:xlink="http://www.w3.org/1999/xlink" viewBox="0 0 380 380" width="380" height="380" version="1.0">
  <g transform="translate(190 190)">
    <circle cx="0" cy="0" r="190" fill="#000"/>
    <line x1="0" y1="-190" x2="0" y2="190" stroke="#fff" stroke-width="1.5"/>
    <line x1="72.71" y1="175.54" x2="-72.71" y2="-175.54" stroke="#fff" stroke-width="1.5"/>
    <line x1="134.35" y1="134.35" x2="-134.35" y2="-134.35" stroke="#fff" stroke-width="1.5"/>
    <line x1="175.54" y1="72.71" x2="-175.54" y2="-72.71" stroke="#fff" stroke-width="1.5"/>
    <line x1="190" y1="0" x2="-190" y2="0" stroke="#fff" stroke-width="1.5"/>
    <line x1="175.54" y1="-72.71" x2="-175.54" y2="72.71" stroke="#fff" stroke-width="1.5"/>
    <line x1="134.35" y1="-134.35" x2="-134.35" y2="134.35" stroke="#fff" stroke-width="1.5"/>
    <line x1="72.71" y1="-175.54" x2="-72.71" y2="175.54" stroke="#fff" stroke-width="1.5"/>
    <g transform="rotate(0)">
      <animateTransform attributeType="xml" attributeName="transform" type="rotate" from="0" to="360" begin="0" dur="8s" repeatCount="indefinite"/>
      <g transform="translate(0 90)">
        <g transform="rotate(0)">
          <animateTransform attributeType="xml" attributeName="transform" type="rotate" from="0" to="-360" begin="0" dur="4s" repeatCount="indefinite"/>
          <circle cx="0" cy="90" r="10" fill="#fff"/>
          <circle cx="63.64" cy="63.64" r="10" fill="#fff"/>
          <circle cx="90" cy="0" r="10" fill="#fff"/>
          <circle cx="63.64" cy="-63.64" r="10" fill="#fff"/>
          <circle cx="0" cy="-90" r="10" fill="#fff"/>
          <circle cx="-63.64" cy="-63.64" r="10" fill="#fff"/>
          <circle cx="-90" cy="0" r="10" fill="#fff"/>
          <circle cx="-63.64" cy="63.64" r="10" fill="#fff"/>
share|improve this answer
Hmmm, I'm sure this passes muster with the rules, but I was, personally, disappointed that you are in fact doing the opposite. Rather than “It looks like the points [are] rotating inside of the circle, but they are actually just moving in straight lines.”, yours implements: “It looks like the points [are] moving in straight lines, but they are actually just rotating inside of the circle.” –  mkoistinen Jul 22 '14 at 0:10
Smoothest answer! –  Derek 朕會功夫 Jul 22 '14 at 3:35
@mkoistinen I see what you mean, but the points really are moving in straight lines. It just happens to be easier to calculate their positions with two rotations :-) –  squeamish ossifrage Jul 22 '14 at 8:02
Did you do it all 'by hand' or did you use any kind of (non-text-) editor? –  flawr Jul 23 '14 at 7:05
@flawr I just used a plain text editor and the calculator in my phone to work out the numbers :-) –  squeamish ossifrage Jul 23 '14 at 7:34


intervaltime changes the FPS (FPS = 1000/intervaltime).
balls changes the # balls.
maxstep adjusts the # steps in a cycle, the larger the 'smoother' it is. 64 should be large enough where it appears smooth.

Modeled as a circle moving, instead of moving the balls along the lines, but the visual effect (should be?) the same. Some of the code is pretty verbose, but this isn't code golf, so...

var intervalTime = 40;
var balls = 8;
var maxstep = 64;

var canvas = $('#c').get(0); // 100% necessary jquery
var ctx = canvas.getContext('2d');
var step = 0;

animateWorld = function() {
    step = step % maxstep;
    var centerX = canvas.width/2 + 115 * Math.cos(step * 2 / maxstep * Math.PI);
    var centerY = canvas.height/2 + 115 * Math.sin(step * 2 / maxstep * Math.PI);

    for (var i=0; i<balls; i++) {
        drawCircle(ctx, (centerX + 115 * Math.cos((i * 2 / balls - step * 2 / maxstep) * Math.PI)), (centerY + 115 * Math.sin((i * 2 / balls - step * 2 / maxstep) * Math.PI)), 10, '#FFFFFF');     


function createBase() {
    drawCircle(ctx, canvas.width/2, canvas.height/2, 240, '#000000');
    for(var i=0; i<balls*2; i++) {
        drawLine(ctx, canvas.width/2, canvas.height/2, canvas.width/2 + 240 * Math.cos(i / balls * Math.PI), canvas.height/2 + 240 * Math.sin(i / balls * Math.PI), '#FFFFFF');

function drawLine(context, x1, y1, x2, y2, c) {
    context.lineWidth = 3;
    context.strokeStyle = c;

function drawCircle(context, x, y, r, c) {
    context.arc(x, y, r, 0, 2*Math.PI);
    context.fillStyle = c;

function drawRect(context, x, y, w, h, c) {
    context.fillStyle = c;
    context.fillRect(x, y, w, h);

$(document).ready(function() {
    intervalID = window.setInterval(animateWorld, intervalTime);
share|improve this answer
It's so smooth! Very nice. –  nneonneo Jul 21 '14 at 20:35
Don't use setInterval for animations, take requestAnimationFrame instead. Modified JSFiddle using requestAnimationFrame. –  klingt.net Jul 22 '14 at 11:00
With just a few parameter tweaks you get a very different thing. –  FreeAsInBeer Jul 23 '14 at 13:09
@KevinL Yep, just noticed that too. Updated. –  FreeAsInBeer Jul 23 '14 at 13:11
@FreeAsInBeer Oh, when you said very different thing, I thought you meant like the ones in jsfiddle.net/z6vhD/100 –  Kevin L Jul 23 '14 at 13:13

CSS animations

A solution using only css animations (see animation on JSFiddle - note that I added the browser specific prefixes in the fiddle so that it can work in most recent versions).

    <div id="w1"></div>
    <div id="w2"></div>
    <div id="w3"></div>
    <div id="w4"></div>
    <div id="w5"></div>
    <div id="w6"></div>
    <div id="w7"></div>
    <div id="w8"></div>

div {
    position: absolute;
    width: 20px;
    height: 20px;
    border-radius: 20px;
    background: red;
    animation-duration: 4s;
    animation-iteration-count: infinite;
    animation-direction: alternate;
    animation-timing-function: ease-in-out;

#w1 { animation-name: s1; animation-delay: 0.0s }
#w2 { animation-name: s2; animation-delay: 0.5s }
#w3 { animation-name: s3; animation-delay: 1.0s }
#w4 { animation-name: s4; animation-delay: 1.5s }
#w5 { animation-name: s5; animation-delay: 2.0s }
#w6 { animation-name: s6; animation-delay: 2.5s }
#w7 { animation-name: s7; animation-delay: 3.0s }
#w8 { animation-name: s8; animation-delay: 3.5s }

@keyframes s1 { from {top: 100px; left:   0px;} to {top: 100px; left: 200px;} } 
@keyframes s2 { from {top:  62px; left:   8px;} to {top: 138px; left: 192px;} } 
@keyframes s3 { from {top:  29px; left:  29px;} to {top: 171px; left: 171px;} } 
@keyframes s4 { from {top:   8px; left:  62px;} to {top: 192px; left: 138px;} } 
@keyframes s5 { from {top:   0px; left: 100px;} to {top: 200px; left: 100px;} } 
@keyframes s6 { from {top:   8px; left: 138px;} to {top: 192px; left:  62px;} } 
@keyframes s7 { from {top:  29px; left: 171px;} to {top: 171px; left:  29px;} } 
@keyframes s8 { from {top:  62px; left: 192px;} to {top: 138px; left:   8px;} } 
share|improve this answer
Fiddle not working for me on latest Chrome =/ –  mkoistinen Jul 22 '14 at 0:14
@mkoistinen - You have to add different prefixes for it to be working in different browsers. (-webkit- for Webkit-based and -moz- for Mozilla-based) Here is the same fiddle with updated prefixes: jsfiddle.net/nBCxz/3 –  Derek 朕會功夫 Jul 22 '14 at 3:30
@mkoistinen You're right. The new fiddle adds all necessary browser prefixes and works on latest Chrome. –  Howard Jul 22 '14 at 4:50
The raw link text is just missing the closing parenthesis - still perfectly usable just letting you know in case you wanted to fix it (I can't as it's less than 6 characters to change). –  trichoplax Jul 23 '14 at 9:51


Here is a pretty straight-forward submission.

animateCircle[n_] := Animate[Graphics[
        phase = #*2 \[Pi]/n;
        line = {Cos[phase], Sin[phase]};
        {Line[{-line, line}],
         Disk[Sin[t + phase]*line, 0.05]}
        ) &,
   PlotRange -> {{-1.1, 1.1}, {-1.1, 1.1}}
  {t, 0, 2 \[Pi]}

If you call animateCircle[32] you'll get a neat animation with 32 lines and circles.

enter image description here

It's completely smooth in Mathematica, but I had to limit the number of frames for the GIF a bit.

Now what happens if you put two discs on each line? (That is, add Disk[-Sin[t + phase]*line, 0.05] to the list within the Map.)

enter image description here

You can also put them 90° out of phase (use Cos instead of -Sin):

enter image description here

share|improve this answer
I dunno what glitches do you mean, probably you need to change {t, 0, 2 \[Pi]} to {t, 0, 2 \[Pi] - 2 \[Pi]/60, 2 \[Pi]/60} so that there won't be two identical frames and change Animate to Table. Then you'll be able to export GIF. –  swish Jul 22 '14 at 7:12
@swish No it actually renders weird additional lines that aren't there and the discs in places where they shouldn't be (and where they never are in the actual result of Animate). I'll try using Table again though. –  Martin Büttner Jul 22 '14 at 7:14
@swish That worked. I thought I tried something like this yesterday, but apparently I didn't. –  Martin Büttner Jul 22 '14 at 7:21

VBScript + VBA + Excel Pie Chart

This will make your processor cry a little but it looks pretty and I believe it works according to spec. I used @Fabricio's answer as a guide to implement the circle movement algorithm.

EDIT: Made some adjustments to improve render speed.

Screenshot of Pie chart

The code:

'Open Excel
Set objX = CreateObject("Excel.Application")
objX.Visible = True

'Populate values
objX.Cells(1, 1).Value = "Lbl"
objX.Cells(1, 2).Value = "Amt"
For fillX = 2 to 17
    objX.Cells(fillX, 1).Value = "V"+Cstr(fillX-1)
    objX.Cells(fillX, 2).Value = "1"

'Create pie
With objX.ActiveChart
    .ChartType = 5 'pieChart
    .SetSourceData  objX.Range("$A$2:$B$17")
End with    

'Format pie
With objX.Selection.Format
    .Fill.ForeColor.RGB = 0 'black
    .Line.Weight = 2
    .Line.Visible = 1
    .Line.ForeColor.RGB = 16777215 'white
End With

'animation variables
pi = 3.14159265358979323846
circle = pi * 2 : l  = 16.0
hlen = l / 2    : cx = 152.0
cy = 99.0       : w  = 90.0
h  = 90.0       : s  = 0.0
Dim posArry(7,1)

While 1 
  For i = 0 to hlen-1
    a = (i / l) * circle
    range = cos(a + s)
    x = cx + cos(a) * w * range
    y = cy + sin(a) * h * range

    If whileInx = 1 Then 
        createOval x, y
    ElseIf whileInx = 2 Then 
    ElseIf whileInx > 2 Then
        ovalName = "Oval "+ Cstr(i+1)
        dx = x - posArry(i,0)
        dy = y - posArry(i,1)
        moveOval ovalName, dx, dy
    End if

    posArry(i,0) = x
    posArry(i,1) = y

  wscript.Sleep 1000/60 '60fps
  whileInx = 1 + whileInx

'create circles
sub createOval(posX, posY)
    objX.ActiveChart.Shapes.AddShape(9, posX, posY, 10, 10).Select '9=oval
    objX.Selection.ShapeRange.Line.Visible = 0
    with objX.Selection.ShapeRange.Fill
       .Visible = 1
       .ForeColor.RGB = 16777215 'white
    end with
end sub

'move circles
sub moveOval(ovalName, dx, dy)
    with objX.ActiveChart.Shapes(ovalName)      
        .IncrementLeft dx
        .IncrementTop  dy
    end with
end sub
share|improve this answer
+1 for masochism –  Von Lion Jul 24 '14 at 12:47
It crashes for me at line 81, error 80070057, "element with the given name does not exist" or something like this (translated back from Hungarian, that's why I don't know the exact error message). –  marczellm Jul 27 '14 at 8:37
Szervusz, @marczellm. I can reproduce that error when I click outside of the chart while it is "animating". You have to allow it focus or the program will error. Otherwise, this may be due to an incompatibility with Office. I'm on Office 2010 on Win7. –  comfortablydrei Jul 28 '14 at 17:08
Office 2007, Win7. Seems like in my case the chart doesn't get focus at all. –  marczellm Jul 29 '14 at 6:50


Each frame is created as an individual gif file using the Fortran gif module at: http://fortranwiki.org/fortran/show/writegif
Then I cheat a little by using ImageMagick to merge the individual gifs into one animated gif.


UPDATE: Set new = .true. to get the following:

enter image description here

program circle_illusion

use, intrinsic :: iso_fortran_env, only: wp=>real64
use gif_util  !gif writing module from http://fortranwiki.org/fortran/show/writegif

implicit none

logical,parameter :: new = .false.

integer,parameter  :: n        = 500  !550  !size of image (square)     
real(wp),parameter :: rcircle  = n/2  !250  !radius of the big circle
integer,parameter  :: time_sep = 5    !deg

real(wp),parameter :: deg2rad = acos(-1.0_wp)/180.0_wp
integer,dimension(0:n,0:n):: pixel     ! pixel values
integer,dimension(3,0:3)  :: colormap  ! RGB 0:255 for colors 0:ncol    
real(wp),dimension(2)     :: xy
integer,dimension(2)      :: ixy
real(wp)                  :: r,t
integer                   :: i,j,k,row,col,m,n_cases,ang_sep
character(len=10)         :: istr

integer,parameter  :: black = 0
integer,parameter  :: white = 1
integer,parameter  :: red   = 2
integer,parameter  :: gray  = 3    
colormap(:,0) = [0,0,0]          !black
colormap(:,1) = [255,255,255]    !white
colormap(:,2) = [255,0,0]        !red
colormap(:,3) = [200,200,200]    !gray

if (new) then
    ang_sep = 5
    n_cases = 3
    ang_sep = 20
    n_cases = 0
end if

do k=0,355,time_sep

    !clear entire image:
    pixel = white      

    if (new) call draw_circle(n/2,n/2,black,n/2)  

    !draw polar grid:    
    do j=0,180-ang_sep,ang_sep
        do i=-n/2, n/2
            call spherical_to_cartesian(dble(i),dble(j)*deg2rad,xy)
            call convert(xy,row,col)
            if (new) then
                pixel(row,col) = gray
                pixel(row,col) = black  
            end if  
        end do
    end do

    !draw dots:
    do m=0,n_cases
        do j=0,360-ang_sep,ang_sep
            r = sin(m*90.0_wp*deg2rad + (k + j)*deg2rad)*rcircle                
            t = dble(j)*deg2rad    
            call spherical_to_cartesian(r,t,xy)
            call convert(xy,row,col)
            if (new) then
                !call draw_circle(row,col,black,10)  !v2
                !call draw_circle(row,col,m,5)       !v2
                call draw_circle(row,col,white,10)   !v3
                call draw_square(row,col,red)        !v1
            end if
        end do
    end do

    !write the gif file for this frame:        
    write(istr,'(I5.3)') k
    call writegif('gifs/test'//trim(adjustl(istr))//'.gif',pixel,colormap)

end do

!use imagemagick to make animated gif from all the frames:
! from: http://thanosk.net/content/create-animated-gif-linux
if (new) then
    call system('convert -delay 5 gifs/test*.gif -loop 0 animated.gif')
    call system('convert -delay 10 gifs/test*.gif -loop 0 animated.gif')
end if

!delete individual files:
call system('rm gifs/test*.gif')


    subroutine draw_square(r,c,icolor)

    implicit none
    integer,intent(in) :: r,c  !row,col of center
    integer,intent(in) :: icolor

    integer,parameter :: d = 10 !square size

    pixel(max(0,r-d):min(n,r+d),max(0,c-d):min(n,c+d)) = icolor

    end subroutine draw_square

    subroutine draw_circle(r,c,icolor,d)

    implicit none
    integer,intent(in) :: r,c  !row,col of center
    integer,intent(in) :: icolor
    integer,intent(in) :: d  !diameter

    integer :: i,j

    do i=max(0,r-d),min(n,r+d)
        do j=max(0,c-d),min(n,c+d)
            if (sqrt(dble(i-r)**2 + dble(j-c)**2)<=d) &
                pixel(i,j) = icolor
        end do
    end do

    end subroutine draw_circle

    subroutine convert(xy,row,col)

    implicit none
    real(wp),dimension(2),intent(in) :: xy  !coordinates
    integer,intent(out) :: row,col

    row = int(-xy(2) + n/2.0_wp)
    col = int( xy(1) + n/2.0_wp)

    end subroutine convert

    subroutine spherical_to_cartesian(r,theta,xy)

    implicit none
    real(wp),intent(in) :: r,theta
    real(wp),dimension(2),intent(out) :: xy

    xy(1) = r * cos(theta)
    xy(2) = r * sin(theta)

    end subroutine spherical_to_cartesian

end program circle_illusion
share|improve this answer
I like the impact 'squish' for the vertical & horizontal elements. –  Portland Runner Jul 25 '14 at 4:20

A compact javascript version, changing the default settings to something different



<canvas id="c" width="400" height="400" />


var v= document.getElementById('c');
var c= v.getContext('2d');
var w= v.width, w2= w/2;
var num= 28, M2= Math.PI*2, da= M2/num;
var bw= 10;
var time= 0;
function draw()
    v.width= w;
    c.fillStyle= 'black';
    c.lineWidth= 1.5;
    c.strokeStyle= c.fillStyle= 'white';
    var a= 0;
    for (var i=0; i< num*2; i++){
        c.lineTo(w2+Math.cos(a)*w2, w2+Math.sin(a)*w2);
        a+= da/2;
    a= 0;
    for (var i=0; i< num; i++){
               w2+Math.sin(a)*Math.sin(time+i*Math.PI/num)*(w2-bw), bw);
        a+= da/2;

function circle(x,y,r)
    c.arc(x, y, r, 0, M2);

share|improve this answer
You made ... a doughnut?? Actually your animation looks nice with smaller dots (try bw=10). Please edit your answer to show your code. Oh, and while you're at it, there's a bug you should fix: replace time+i*0.39*0.29 with time+i*Math.PI/num in the trig calculations so that the coordinates are calculated correctly for any value of num. (P.S. Updated JSFiddle here. And welcome to codegolf.stackexchange.com) –  squeamish ossifrage Jul 22 '14 at 21:59
I just wanted to make something different (like the turtles one). Newbie here in codegolf :) Oh, and thank you for the formula :D I just did it in a hurry and tried random values, didn't stop a minute to get to the correct formula :P –  Diego Jul 23 '14 at 11:00
+1 Small change for a little visual fun: http://jsfiddle.net/9TQrm/ or http://jsfiddle.net/Wrqs4/1/ –  Portland Runner Jul 25 '14 at 4:17

Just for fun with PSTricks.

enter image description here



% static point
% #1 : half of the number of points
% #2 : ith point

% oscillated point
% #1 : half of the number of points
% #2 : ith point
% #3 : time parameter

% single frame
% #1 : half of the number of points
% #2 : time parameter
    \pstVerb{/I2P {AlgParser cvx exec} bind def}%
    \foreach \i in {1,...,#1}{\psline[linecolor=yellow](!\x[#1,\i] I2P \y[#1,\i] I2P)(!\x[#1,\i] I2P neg \y[#1,\i] I2P neg)}
    \foreach \i in {1,...,#1}{\pscircle*[linecolor=white](!\X[#1,\i]{#2} I2P \Y[#1,\i]{#2} I2P){2pt}}   

\foreach \t in {0,...,24}
    \Frame{1}{2*Pi*\t/25} \quad \Frame{2}{2*Pi*\t/25} \quad \Frame{3}{2*Pi*\t/25} \quad \Frame{5}{2*Pi*\t/25} \quad \Frame{10}{2*Pi*\t/25}
share|improve this answer
+1 for using LaTeX! –  Tengyu Liu Jul 29 '14 at 18:43
@TengyuLiu: :-) Thanks. –  kiss my armpit Jul 29 '14 at 18:47

Mandatory C64 version.

Copy&paste in your favorite emulator:

C64 version

1 print chr$(147)
2 poke 53281,0
3 for p=0 to 7
5 x=int(11+(cos(p*0.78)*10)):y=int(12+(sin(p*0.78)*10))
6 poke 1024+x+(y*40),15
9 next p
10 for sp=2040 to 2047:poke sp,13:next sp
20 for i=0 to 62:read a:poke 832+i,a:next i
30 for i=0 to 7:poke 53287+i,i+1:next i
40 rem activate sprites
50 poke 53269,255
60 an=0.0
70 rem maincycle
75 teta=0.0:k=an
80 for i=0 to 7
90 px=cos(k)*64
92 s=i:x=px*cos(teta): y=px*sin(teta): x=x+100: y=y+137: gosub 210
94 teta=teta+0.392699
95 k=k+0.392699
96 next i
130 an=an+0.1
140 goto 70
150 end
200 rem setspritepos
210 poke 53248+s*2,int(x): poke 53249+s*2,int(y)
220 return
5000 data 0,254,0
5010 data 3,199,128
5020 data 7,0,64
5030 data 12,126,96
5040 data 25,255,48
5050 data 59,7,152
5060 data 52,1,200
5070 data 116,0,204
5080 data 120,0,100
5090 data 120,0,100
5100 data 120,0,100
5110 data 120,0,36
5120 data 104,0,36
5130 data 100,0,108
5140 data 54,0,72
5150 data 51,0,152
5160 data 25,131,16
5170 data 12,124,96
5180 data 4,0,64
5190 data 3,1,128
5200 data 0,254,0
share|improve this answer

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