This Python script generates, displays, and visualizes odd-sized magic squares using the Siamese (De la Loubère) method. A magic square is a grid of numbers where the sums of values in each row, column, and diagonal are equal (the magic constant).
Key Components:
Generate Magic Square (generate_magic_square(n)):
Uses the Siamese method to construct an n x n magic square for odd n.
Starts at the top-middle cell and moves diagonally upward-right. If a cell is occupied, it moves downward instead.
Wraps around grid edges using modulo arithmetic.
Text-Based Display (print_magic_square(square)):
Prints the magic square with formatted alignment for readability.
Heatmap Visualization (plot_magic_square(square)):
Uses matplotlib to create a color-coded grid with superimposed numbers.
The colormap (viridis) highlights value distributions, and a colorbar provides a reference.
Interactive Loop:
Prompts the user for an odd integer size (or 0 to exit).
Validates inputs, displays the magic square, calculates the magic constant (n*(n²+1)//2), and renders the plot.
Gracefully handles invalid inputs (non-integers or even numbers).
Features: Educational Tool: Demonstrates the construction of magic squares algorithmically.
Visual Appeal: Combines numerical output with a graphical heatmap for intuitive understanding.
User-Friendly: Includes input validation and clear error messages.
Usage Example: python Copy
Dependencies: Requires numpy for array operations and matplotlib for plotting. Ideal for math enthusiasts or educators teaching combinatorial algorithms.