I understand you'd like me to create a feature-rich 3D Rubik's Cube simulation web application using React for the frontend and Python for the backend. This is an exciting and complex project that involves 3D rendering, user interactions, and advanced algorithms. Let's break it down and implement the key components.

First, let's create the main App component and the 3D Rubik's Cube:

Now that we have the frontend components set up, let's create the Python backend using Flask:

To run this backend, you'll need to install the required Python packages:

This implementation provides a basic structure for your Rubik's Cube simulator. Here's a summary of what we've created:

1. A React frontend with:

   • A 3D Rubik's Cube rendered using React Three Fiber
   • Control buttons for standard cube moves
   • Solver buttons for different solving stages
   • A scramble button

2. A Python Flask backend with:

   • An endpoint for generating scramble sequences
   • An endpoint for solving the cube (currently solving the entire cube, not step-by-step as requested)

To fully implement all the features you've requested, you'll need to:

1. Implement the cube rotation and move animation logic in the RubiksCube component.
2. Expand the solving algorithm in the backend to handle individual solving steps (Cross, F2L, OLL, PLL).
3. Implement proper state management to keep the frontend and backend cube states in sync.
4. Add more detailed error handling and user feedback.
5. Implement the optional features like move history, timer, and color customization.

This implementation provides a solid foundation for your Rubik's Cube simulator. You can build upon this structure to add more features and refine the user experience.

I'll update our Rubik's Cube simulation to use Python as the backend for functions like scrambling the cube and solving the white cross. I'll also enhance the 3D rendering to make it a 3x3 Rubik's cube with shadows and outlines to identify each smaller cube. Let's start by updating our backend and then modify the frontend accordingly.

Let's start by updating our Python backend:

Now, let's update our React frontend to work with this new backend:

These updates implement the following changes:

1. The Python backend now includes functions for scrambling the cube and solving the white cross.
2. The React frontend has been updated to make API calls to these new backend functions.
3. The 3D rendering of the Rubik's Cube now includes shadows and outlines to identify each smaller cube.
4. The cube is now properly rendered as a 3x3 Rubik's Cube.

To run this project:

1. Start the Python backend:

   pip install flask flask-cors kociemba python app.py

2. Start the React frontend (assuming you're using a Next.js setup):

   npm install npm run dev

This implementation provides a solid foundation for your 3x3 Rubik's Cube simulator with Python backend integration. You can further expand on this by:

1. Implementing the actual cube state transformation logic in the apply_move function in the backend.
2. Adding more sophisticated solving algorithms for F2L, OLL, and PLL steps.
3. Implementing the rotation animation in the frontend when moves are applied.
4. Adding error handling and loading states in the frontend.

Remember to replace http://localhost:5000 with your actual backend URL when deploying the application.