JW's Spirograph application

r3,-4 cRed

Draws a simple pattern using wheel rates 3 and −4, which has a symmetry of 3 −(−4) = 7 in red. Some more symmetry 7 patterns: −6,1 , −5,2 , −4,3 , −3,4 , −2,5 , −6,1 , 1,8 , 8,15 , 15,22 , 23,30 .

r3,-4 cRed,Blue,Green,Purple,Red,-7

The same pattern, drawn in the sequence of colours Red, Blue, Green, Purple, Red, repeated 7 times to match the symmetry of the pattern.

r2,-3 bCoolBlack cWhite,Yellow,White,-5 da0,2 n24 ds.99

Draws a pattern with 5-fold symmetry, repeated 24 times, rotated (da) and slightly smaller (ds).

r1,-6 dr1,1 n3 cBlue,Green,Red fP ds.9

Superimposes three different 7‐fold patterns using the 'dr' parameter to increment the wheel rates.

n21 da0,.6 ds.98

Draws the default pattern, but with the phase of the second wheel changing from 0° to 12° with the pattern getting slightly smaller (ds.98) after each step.

r3,-4,24 w7,3,2 cAmber,Yellow,Green,White,Amber,-7 bDarkGreen

Another 7-fold symmetry pattern, but now with three wheels. Try changing the value of the 3rd wheel rate to see how the symmetry is destroyed, "r3,-4,23" for instance.

fA cFuchsia,Fawn,-6 bBlack n360 da0,1 i50 r2,-5,9

This pattern is based on three wheels with rates 2, -5 and 9, the differences being −7 and 7, so the pattern will have 7‐fold symmetry. The "n360" parameter, combined with "da0,1" causes the phase of the second wheel to vary from 0° to 359° before restarting at 0°, which drives the animation. The "fA" parameter causes the screen to be refreshed between each pattern, creating the animation effect. "i50" indicates we would like the animation to refresh every 50ms, twenty frames per second.

r-4,7,117 w5,3,0 dw0,0,.001 n2000 p10000 da.1,0,0 fA bForestGreen cCyan,Yellow,DarkBlue,Cyan,-11 i50

This animation varies the size of a third wheel (dw) while rotating the whole pattern (da).

r-4,7,117 w10,6,1 n3600 p10000 da.1,0,.1 fA bOceanBoatBlue cWhite,Black,-11 i50

This example is similar to the previous one except that now the movement is created by varying the phase of the third wheel, rather than its size.

fDA da0,1,.02 n18000 i50 r5,-2,500 w15,10,2 p10000

This example shows how to combine the dashed drawing mode with high wheel‐rates to create interesting animations. There are 10,000 points in the pattern but the third wheel is rotating at 500, so there will only be 20 points per cycle, which combined with the dashed flag (fD) draws 10 disjointed lines.

You can experiment by changing the rate of this 3rd wheel to different fractions of 10000, such as 800, 1250, 1600, 2400, 2500 or 5000.

fDAP w5,4,3 r-1,-200,201,199 p1200 da-0.013,.017,0.023 n3600 cRed,Magenta,Green,Yellow,Purple,Cyan,Red,1000 bBlack

Another animation. Here all the wheel rates are very large and the result looks nothing like a traditional spirograph. The 'P' in 'fDAP' means that the colours change as the patterns progress rather than within each pattern.

Interesting variants can be created by changing, the 'r' parameter, 'r-1,-101,199,203' or 'r-1,201,196,206' for instance.

Or other colour schemes: Scheme 1, Scheme 2.

You can speed the animation up by choosing smaller 'i' values, I tried 'i10' which requests 100 frames per second, though my PC could only manage about 30‐40.

fFA r-1,7,47 w5,4,2 p40 dp8 n120 i500 bPaynesGrey cBlack,PaleRobinEggBlue

This animations varies the number of points and demonstrates the "fill" flag. For small numbers of points the patterns are quite angular but as the number of points increases they converge on the smoothr pattern.