another hypotrochoid

Had another one lurking on my desktop:

and here’s the gnuplot code to generate it:

set terminal svg size 400,400
 set output "fig-spiro11.svg"
 set size ratio -1
 set nokey
 set noxtics
 set noytics
 set noborder
 set parametric
 x(t)=(R-r)*cos(t) + p*cos((R-r)*t/r)
 y(t)=(R-r)*sin(t) - p*sin((R-r)*t/r)
 R=100.0; r=-37.0; p=50.0
 set samples 8001
 plot [t=0:320*pi] x(t),y(t)

some svg hypotrochoids

Just by messing around with the simple gnuplot script in the article Plotting the spirograph equations with ‘gnuplot’, I made: