This section archives basic mandalas patterns. Every pattern is based on one parametric curve. Thanks to the polar coordinate system, each point on a mandala is determined only by one parameter $$$\alpha$$$. For each point, the function $$$r(\alpha)$$$ calculates its distance from mandalas center and the function $$$\theta(\alpha)$$$ its angle with respect to Mandalas vertical axis.
For instance: $$$
\left \{ \begin{array}{r c l}
\theta(\alpha)& = &0.2\times\tan{(0.1+k_{a}\cdot\alpha)}^* \\
r(\alpha)& = &0.2\times\cos^2{(\alpha)}+\frac{t}{3}
\end{array}\right .$$$
*If not specified, $$$\theta(\alpha)=\alpha$$$.
The constants $$$k_{i}$$$ are determined by the mouse event (mouse) or touch event (active screens).
$$$t$$$ represents time for self-animated mandalas.