Ornamental Parametric Figures

a

0.8

b

10.

thickness

0.02

The components of these ornamental figures are curves with the parametric equations:

x(t)=sin(t/2)-asin(bt)cost

,

y(t)=cos(t/2)-asin(bt)sint

.

The adjustable parameters

a

and

b

can produce a large number of different forms.

The aesthetic effect is achieved by the appearance of different types of symmetry inherent in the equations. Both simple and complex patterns can be seen. Especially interesting results can be obtained by varying

b

manually with

a

fixed at 1.2.