Loxodrome Art
Loxodrome Art
The parametric equation of a loxodrome on the unit sphere can be expressed as . This family of curves is parametrized by and . In this Demonstration, you can continuously vary the parameter and see curves obtained by using values of the parameter spaced evenly from to .
(x,y,z)=,,1-
cos(t)((4a))
θt
4+
2
a
2θt
sin(t)((4a))
θt
4+
2
a
2θt
8
4+
2
a
2θt
a
θ
a
m
θ
θ
min
θ
range
Varying the parameter or the number of curves , or changing the range of the bearing angle , yields some interesting artistic images.
a
m
θ