Hypnotic Pendulum

This isn't just an animation; it's a demonstration of Simple Harmonic Motion. In a real physical setup, you would have a series of pendulums with successively shorter string lengths.

The period of a pendulum (T) is determined by its length (L): T ≈ 2π√(L/g). By carefully tuning the lengths, we ensure that each pendulum completes a specific number of oscillations per minute. For example:

• Pendulum 1: 51 oscillations/min
• Pendulum 2: 52 oscillations/min
• Pendulum 3: 53 oscillations/min

This slight difference in frequency creates the "wave" effect.

The beauty of the Pendulum Wave is its cycle. They start in sync (a straight line). As time passes, they drift out of phase due to their different speeds, creating:

• Traveling Waves: Apparent snake-like movement.
• Standing Waves: Crossing patterns.
• Chaos: Complete disarray.
• Re-alignment: Eventually, the math dictates they must all align again (usually after 60 seconds in a tuned set).

Humans are pattern-seeking machines. Our brains are constantly trying to predict the motion of objects. In the Pendulum Wave, the pattern is constantly evolving.

Just as your brain locks onto one pattern (e.g., "It's a snake"), the phase shifts, and it becomes a double-helix, then a chaotic cloud. This constant engagement of the brain's prediction circuits releases Dopamine when a pattern is successfully recognized, making the viewing experience deeply satisfying and attention-holding.