Rubik's Cube Simulator and Visualizer

This repository contains three modules:

1. RubiksCube.py:

   • A Rubik's Cube simulator using a group theory approach to represent the cube and its operations using matrix algebra.
   • The cube is represented as a 1D numpy array, and operations on the cube are represented as permutation arrays.
   • This allows for efficient and mathematically rigorous manipulation of the cube's state.
   • Includes functionality to create, scramble, rotate, undo, redo moves, and save or load the state of the cube.

2. VisualizeCube.py:

   • A Rubik's Cube visualizer using matplotlib.
   • Provides a visual representation of the cube's state and interaction through terminal input.
   • Allows users to rotate the cube, scramble it, save the state, and load a saved state through terminal commands.

3. PermutationMatricesExamples.py:

   • Provides example lines of code to demonstrate how to work with permutation matrices represented as 1D numpy arrays.
   • Includes examples of converting between permutation arrays and dense numpy matrices, multiplying permutation matrices, transposing permutation matrices, and multiplying permutation matrices onto column vectors.
   • Shows how to represent the identity matrix in this format.

How to Use

To use the simulator and visualizer, follow these steps:

1. Install the required packages:

   pip install numpy matplotlib

2. Run the visualizer:

   python VisualizeCube.py

Classes and Functions

RubiksCube.py

• Classes:

  • RubiksCube: A class to represent and manipulate a Rubik's Cube, including methods for rotating, scrambling, undoing, redoing moves, and saving and loading the cube's state.

• Functions:

  • _site_pairs(S: int) -> Tuple[List[np.ndarray], List[np.ndarray]]: Generates pairs of site indices for rotating planes about the x or z axes.
  • _create_rotation_operators(S: int) -> np.ndarray: Constructs rotation operators along the x, y, and z axes.
  • _create_win_permutations(rotation_operators: np.ndarray) -> np.ndarray: Generates permutation operators for solved states.

VisualizeCube.py

• Functions:
  • display_cube(cube, ax) -> None: Displays the current state of the Rubik's Cube using matplotlib.
  • play() -> None: Initiates the Rubik's Cube game, prompting the user for the cube size and allowing interaction through terminal input.
  • main() -> None: The main function to start the game by prompting the user for the cube size.

PermutationMatricesExamples.py

• Examples:
  • Converting a permutation array to a dense numpy matrix representation.
  • Converting a dense numpy matrix back to a permutation array.
  • Multiplying two permutation matrices.
  • Transposing a permutation matrix.
  • Multiplying a permutation matrix onto a column vector.
  • Representing the identity matrix in permutation array format.