This took about a month and was fun to program, since I'm learning about trigonometry.

Code:

FnOff
Radian
Param
Disp "SPIROGRAPH"
Disp "R=BIG CIRCLE"
Disp "S=SMALL CIRCLE"
Disp "D=PEN DISTANCE"
Prompt R,S,D
2π*S/gcd(R,S)→Tmax
0→Tmin
π/48→Tstep
(R-S+D)*-1.5→Xmin
(R-S+D)*1.5→Xmax
(R-S+D)*-1.5→Ymin
(R-S+D)*1.5→Ymax
"(R-S)cos(T)+Dcos(((R-S)/S)T)"→Str1
"(R-S)sin(T)-Dsin(((R-S)/S)T)"→Str2
String>Equ(Str1,X1T
String>Equ(Str2,Y1T

To make it draw faster, lower the Tstep. Know that doing this also makes the drawing less curved and more jagged and rushed.
Examples
{R,S,D}
{6,2,2}=3-leafed clover
{12,5,8}=complex floral pattern
{20,7,10}=intricate web
  
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