The Cardioid is defined by these equations:
c(t) = RR * [ cos(t)+cos(2t)/2, sin(t)+sin(2t)/2 ]
Of course it is a special case of the
with frequency = 2 and stick = 1. For small frequency values the rolling curves
have individual names (cardioid, nephroid, deltoid, astroid).
The curves drawn with other stick lengths by the same rolling motion
are in general called trochoids; here they are called limacons.
The demo shows at each moment two consecutive positions of the dots. Therefore
the image does not look random but suggests a rotation of the "moving plane".
This page emphasizes that the same rolling motion allows to draw many curves,
one can choose any point of the plane attached
to the rolling wheel as drawing pen. This plane is emphasized by the square
of random dots. The points near the rolling wheel
move almost on cardiods, all others on limacons. The dots near the stick
move tangential to the curves.
The simplest rolling curve is the Cycloid.
Watch how the caustic rotates when the normals are tilted.