Vibrations

[bobnik]

Chladni Figure ("Vibration") Shape

Adds a new shape that generates Chladni figure patterns - the nodal line patterns formed when vibrating plates are covered with sand. Sand collects along lines where amplitude is zero, creating symmetric geometric patterns.

Three methods for generating patterns:

Method	Description
Interference	Classic two-mode superposition with 13 combination modes (add, subtract, beat, grid, rings, etc.)
Harmonic	Multi-mode sum with decay weighting for complex organic patterns
Excitation	Modal response to initial displacement (our own creation; produces some cool patterns)

See README.md for more info.

Key Features

• Configurable contour levels (1-5)
• Boundary conditions: free (cos) vs fixed (sin)
• 13 superposition modes for interference method
• Rectangular and circular geometries
• Complexity/decay controls for harmonic method
• Multiple excitation types: dome, mosaic, cell

The combinations are extremely varied - play around with various options to see how the pattern changes.

[jeffeb3]

This works well. Pretty interesting shapes, for sure.

If I choose the interference pattern, it disappears when M=N. I feel like we hit that in another pattern. Did we just let it go? Or did we find a way to restrict that case in the inputs?

Either way, this is good to merge.

[bobnik]

If I choose the interference pattern, it disappears when M=N. I feel like we hit that in another pattern. Did we just let it go? Or did we find a way to restrict that case in the inputs?
Fixed. Will merge.