# Wolfram Mathematica

## Laminae of a Different Shape

The "Lamina" entity domain contains more than 100 plane regions with a large number of precomputed properties. Here is a random sampling of some of them.

A detailed set of properties is also available for each curve.

Lamina entities are grouped into more than 25 classes.

One common and important class is polygonal laminae.

As already seen in the random sampling of laminae shown previously, in addition to standard named plane regions, mathematical formulations and properties are also available for a number of prominent logos.

This list includes the plane region resembling the insignia of a famous superhero.

This lamina has the slightly complicated (but under the circumstances, not as complex as one might expect) description as a set of inequalities.

Somewhat surprisingly, the bat-area can be computed exactly.

With a little bit of computation using the power of the Wolfram Language, you can even combine the forces of two superheroes to meld their logos into a higher-dimensional composite logo. Begin by finding the associated scales.

Now retrieve the bat- and super-regions in the plane.

Finally, meld across dimensions and display the result.

Click the output displayed to see the pandimensional super-bat insignia rotate in 3D.

Additional unconventional mathematical laminae associated with various shapes are included in the "Lamina" entity domain.

The "pirate face" lamina has the following appearance.

It can be plotted as a function of a (large number) of variable parameters.

Choosing a nice set of defaults results in a plane region corresponding to a happy pirate.

On the other hand, perturbing these values slightly gives a slightly perturbed pirate face.