Cardioid and Limacons
Draw several curves with the same rolling motion

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 Epicycloids 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".