Question

How many spheres are rotating in the space shown below?

Hint:

When dealing with structure-from-motion animations, focus on the center and the boundaries of the motion fields. This helps distinguish overlapping structures rotating at different speeds.

Answer 1

Correct Answer: 2

Step 1: Understanding the Question:
This question involves structure-from-motion (the kinetic depth effect).
A set of moving 2D dots is perceived as one or more 3D rotating spheres.
We need to determine how many independent spheres are represented by the coherent motion of these dots.

Step 2: Key Formula or Approach:
1. Group dots that move together in phase (sharing the same angular velocity, axis of rotation, or sinusoidal velocity profile).
2. Identify distinct spherical surfaces by isolating boundaries where dot trajectories diverge or rotate in opposite directions.

Step 3: Detailed Explanation:
1. Visual motion processing allows the human brain to reconstruct 3D shapes from 2D coordinate projections over time.
2. Looking closely at the animated field of dots, we can separate them into two distinct groups:
- Group 1: A larger outer sphere rotating about a vertical or slightly tilted axis.
- Group 2: A smaller, concentric inner sphere rotating in a different direction (or at a different speed).
3. This creates a nested visual illusion consisting of exactly 2 rotating spheres.

Step 4: Final Answer:
There are 2 spheres rotating in the space.