import numpy as np
import math

class HoloBuffer:
    def __init__(self, n_dim, buffer_size):
        """
        Initializes the HoloBuffer.

        Args:
            n_dim: The dimensionality of the input data stream (Volume).
            buffer_size: The size of the Boundary array (surface).
        """
        self.n_dim = n_dim
        self.buffer_size = buffer_size
        self.boundary = np.zeros((buffer_size,) + (n_dim - 1) * (1,)) # Boundary array
        self.bekenstein_area = buffer_size  # Approximation for area.  Actual area calculation would be more complex.
        self.max_entropy = self.bekenstein_area / 4.0
        self.fractal_hash_depth = int(math.log(buffer_size, 2)) # Fractal hashing depth based on buffer size.

    def fractal_hash(self, data_point, depth):
        """
        Simulates fractal hashing for dimensional reduction.
        Each bit of the hash determines a sub-region of the boundary array.
        """
        hash_value = 0
        for i in range(depth):
            if data_point[i] > 0:  # Simple example: use component value
                hash_value += 2**i
        return hash_value % self.buffer_size

    def encode(self, data_stream):
        """
        Encodes the N-dimensional data stream onto the (N-1) dimensional Boundary array.

        Args:
            data_stream: A list or array of N-dimensional data points.
        """
        if len(data_stream) * np.prod(np.array(data_stream[0].shape)) > self.max_entropy:
            raise ValueError("Data exceeds Bekenstein Bound. Cannot encode.")

        for data_point in data_stream:
            index = tuple(self.fractal_hash(data_point[i], self.fractal_hash_depth) for i in range(self.n_dim - 1))
            self.boundary[index] += data_point[-1]  # Store the Nth dimension value on the boundary.

        return self.boundary

    def decode(self, encoded_boundary):
        """
        Decodes the data from the Boundary array. This is a simplified approximation.
        """
        decoded_data = []
        for i in range(self.buffer_size):
            # This is a very simplified decoding.  A true reconstruction would
            # require knowing the original data stream structure.
            decoded_data.append(encoded_boundary[i])
        return decoded_data


# Example Usage
if __name__ == '__main__':
    n_dim = 3
    buffer_size = 64
    holo_buffer = HoloBuffer(n_dim, buffer_size)

    # Generate some sample 3D data
    data_stream = np.random.rand(10, n_dim)

    # Encode the data
    encoded_boundary = holo_buffer.encode(data_stream)

    # Decode the data
    decoded_data = holo_buffer.decode(encoded_boundary)

    print("Original Data Shape:", data_stream.shape)
    print("Encoded Boundary Shape:", encoded_boundary.shape)
    print("Decoded Data Shape:", decoded_data.shape)