Equation-driven smoothly shaded concentric shapes Background
Looking to create interesting video transitions (in grayscale).
Problem
Given equations that represent a closed, symmetrical shape, plot the outline and concentrically shade the shape towards its centre.
Example
Consider the following equations:
x = 16 * sin(t)^3
y = 13 * cos(t) - 5 * cos(2 * t) - 2 * cos(3 * t) - cos(4 * t)
t = [0:2 * pi]

When plotted:

When shaded, it would resemble (not shown completely shaded, but sufficient to show the idea):

Notice that shading is darkest on the outside (e.g., #000000 RGB hex), then lightens as it fills to the centre. The centre would be a white (e.g., #FFFFFF) dot.
Questions


*

*What would be the most expedient way to produce high-resolution, concentrically shaded grayscale images, such as the shaded heart above?

*What are such closed, symmetrical shapes formally called?


Thank you!
Ideas


*

*Use GNUPlot

*Use R

 A: I suspect this is not quite what you're looking for*, but my first idea was to draw line segments from some central point, such as the origin, to various points on the curve, shading the line segment from white at the central end to black at the curve end.  Here is the Mathematica code and the result for your heart-shaped curve, using the origin as the central point, and drawing line segments for $t$ from $0$ to $2\pi$ in steps of $\frac{\pi}{1200}$:
Graphics[Table[
  Line[{{0, 0}, {16 Sin[t]^3, 
     13 Cos[t] - 5 Cos[2 t] - 2 Cos[3 t] - Cos[4 t]}}, 
   VertexColors -> {White, Black}], {t, 0, 2 \[Pi], \[Pi]/1200}]]


* I don't think this is what you're looking for particularly because I don't think it's all that expedient; beyond that, I wouldn't call this concentrically-shaded, exactly, either; also, I have no idea what such shapes are formally called.

Here's a second thought, which is to graph your curve in $k\%$ black, scaled by a factor of $k\%$.  Again, here's Mathematica code and the result with 400 steps from black to white (I don't know what's causing the diagonal line artifacts):
Show[Table[
  ParametricPlot[(1 - k) {16 Sin[t]^3, 
     13 Cos[t] - 5 Cos[2 t] - 2 Cos[3 t] - Cos[4 t]}, {t, 0, 2 \[Pi]},
    PlotStyle -> GrayLevel[k], Axes -> None], {k, 0, 1, 0.0025}]]


