task0_promt.txt

Act as an expert Python developer specialized in physics simulations and 3D graphics. Your goal is to implement "Task 0" of my assignment.

### ASSIGNMENT DESCRIPTION (TASK 0):
"Implement a 3d particle simulation inside of a cube. The number of particles inside of the cube should be controllable interactively via a slider. Initially, particles (represented as small 3d spheres) will be scattered randomly inside the cube. Their initial velocity vectors will be set up randomly as well.
Collisions between particles and with the inside walls of the cube need to be handled.
We consider the cube as being split into n * n smaller subcubes. The purpose is to compute the entropy of each of the subcubes using either the Boltzmann or Shannon techniques or both and to use a colour spectrum to depict each subcube's entropy in real time."

### TECHNICAL CONSTRAINTS & REQUIREMENTS:
1. Language & Libraries: Use Python. Strictly use `vpython` for the 3D rendering, the interactive UI slider, and the main simulation loop. Use `numpy` for efficient vector math (positions, velocities).
2. Physics: Implement basic elastic collisions for particle-wall and particle-particle interactions.
3. Subcubes & Entropy:
   - Logically divide the main bounding cube into a grid of smaller subcubes (e.g., 3x3x3).
   - In the update loop, track which particles are in which subcube.
   - Calculate the entropy (choose either Boltzmann or Shannon based on particle speed or density state) for each subcube.
4. Visuals: Render a visual indicator for the subcubes (e.g., semi-transparent boxes or grid lines) and dynamically update their color in real-time based on the computed entropy value using a color gradient (e.g., blue for low entropy, red for high entropy).

Please provide the complete, runnable Python code for this simulation.