Valentines Day is coming up, and you less artistic folk might want to make a nice heart picture to send to your girlfriend. A parametrization of a heart shape is the following: $$x = 16\text{sin}^3(t)$$ $$y = 13\text{cos}(t) - 5\text{cos}(2t) - 2\text{cos}(3t) - \text{cos}(4t)$$The heart is drawn as $t$ ranges from $0$ to $2\pi$. How you increment $t$ can alter the picture in cool ways. Interestingly, the area enclosed is exactly $180\pi$
Blue, scale = $\frac{3}{2}$, $ t = 1, 2, 3, ...$
Red, scale = 1, $ t = \frac{1}{2}, \frac{2}{2}, \frac{3}{2}, ...$
Black, scale = $\frac{3}{5}$, $ t = \frac{1}{100}, \frac{2}{100}, \frac{3}{100}, ...$
Green, scale = $\frac{1}{5}$, $t = k(\pi - .01), \; k = 0,1,2, ...$
Green, scale = $\frac{1}{5}$, $t = k(\pi - .01), \; k = 0,1,2, ...$
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