Let's say you want to draw a hypocycloid (spirograph) with a turtle. I use a parametric equation for each of the circles and combining them to find the x and y position of the points on the curve then telling the turtle to goto(x,y)

This works fine, however it is NOT in the intended "spirit" of drawing with a turtle. Drawing with a turtle is about "relative" navigation. Consider two ways to draw a circle:

for 0<t<2pi:
goto(rcos(t), rsin(t))

repeat 100:
forward 2
right 2