Miller's madness is the plane curve defined by the parametric equations
 |  |  |
(1)
|
 |  |  |
(2)
|
where 
is measured in radians. Dewdney (1988, p. 121) named
the curve after Stanley S. Miller, who supplied it. The illustration above shows
the portion traced over 
.
The curve is related to a Lissajous curve, but each coordinate contains two trigonometric
functions with distinct frequencies. Both coordinates are periodic
functions with least period 
. This follows because the frequencies are 
, 
, 
, and 
, and each coordinate's pair of integer numerators has
greatest common divisor 1. The complete
curve is therefore traced over 
.
