3D-Ulam-Spiral.rs

3D-Ulam-Spiral.rs

// a 3D Ulam Spiral 
// projected onto a 2D grid,
// marking primes with their Z-index.

/// Generates a boolean vector where `is_prime[i]` is true if `i` is a prime number (Sieve of Eratosthenes).
fn sieve_of_eratosthenes(max_value: usize) -> Vec<bool> {
    if max_value < 2 { return vec![]; }
    let mut is_prime = vec![true; max_value + 1];
    is_prime[0] = false;
    is_prime[1] = false;
    let mut p = 2;
    while p * p <= max_value {
        if is_prime[p] {
            let mut i = p * p;
            while i <= max_value {
                is_prime[i] = false;
                i += p;
            }
        }
        p += 1;
    }
    is_prime
}

/// Generates the N x N grid projection by running the spiral across multiple Z-planes (max_z).
fn generate_3d_projection(n: usize, max_z: usize) -> (Vec<Vec<char>>, usize) {
    if n == 0 || max_z == 0 { return (vec![], 0); }

    let dim = if n % 2 == 0 { n + 1 } else { n };
    let total_cells = dim * dim * max_z;
    let is_prime = sieve_of_eratosthenes(total_cells);
    let mut current_num = 1;
    
    // Initialize the 2D grid with a placeholder character (e.g., space or dot)
    let mut grid: Vec<Vec<char>> = vec![vec!['.'; dim]; dim];

    for z in 0..max_z {
        // --- Spiral Setup for the current Z-plane ---
        let mut x = dim / 2;
        let mut y = dim / 2;
        let mut step_length = 1;
        let mut turns_made = 0;
        let mut direction = 0; // 0: Right, 1: Up, 2: Left, 3: Down
        let dx = [1, 0, -1, 0];
        let dy = [0, -1, 0, 1];
        let cells_in_plane = dim * dim;
        let mut cells_filled_in_plane = 0;

        // Handle the center cell first
        if current_num <= total_cells {
            if current_num < is_prime.len() && is_prime[current_num] {
                // Mark center cell with Z-index
                // Use the Z index modulo 10 to get a single digit '0' through '9'
                grid[y][x] = (b'0' + (z % 10) as u8) as char;
            } else {
                // If not prime, leave the existing mark (or dot if it's the first time)
                if grid[y][x] == ' ' || grid[y][x] == '.' {
                    grid[y][x] = '.';
                }
            }
            current_num += 1;
            cells_filled_in_plane += 1;
        }
        
        // --- Core Spiral Generation for this Z-plane ---
        while cells_filled_in_plane < cells_in_plane {
            for _ in 0..step_length {
                if current_num > total_cells {
                    return (grid, total_cells);
                }

                // Update position (x, y)
                x = (x as isize + dx[direction]) as usize;
                y = (y as isize + dy[direction]) as usize;

                // Mark the cell if it's a prime
                if current_num < is_prime.len() && is_prime[current_num] {
                    // Mark with Z-index
                    grid[y][x] = (b'0' + (z % 10) as u8) as char;
                } else {
                     // If not prime, leave the existing mark (or dot if it's the first time)
                    if grid[y][x] == ' ' || grid[y][x] == '.' {
                        grid[y][x] = '.';
                    }
                }
                
                current_num += 1;
                cells_filled_in_plane += 1;
                
                if cells_filled_in_plane >= cells_in_plane { break; }
            }
            
            if cells_filled_in_plane >= cells_in_plane { break; }

            // Change direction and increase step length
            direction = (direction + 1) % 4;
            turns_made += 1;
            if turns_made % 2 == 0 {
                step_length += 1;
            }
        }
    }

    (grid, total_cells)
}

/// Prints the resulting Ulam spiral projection to the console.
fn print_projection(grid: &Vec<Vec<char>>, max_num: usize, n: usize, max_z: usize) {
    println!("\n--- 3D Ulam Spiral Projection onto X-Y Plane ---");
    println!("Grid Size: {n}x{n} | Z-Planes: 0 to {} | Max Number: {}", max_z - 1, max_num);
    println!("-----------------------------------------------");
    
    for row in grid {
        for &cell in row {
            print!("{} ", cell);
        }
        println!();
    }
    println!("-----------------------------------------------");
    println!("Key: '.' = Composite or Unmarked Prime (Z=0)");
    println!("     '0' - '{}' = Prime from that Z-Plane Index", max_z.min(9));
}


fn main() {
    let n = 38; // Size of the 2D plane (N x N)
    let max_z = n*n; // Number of Z-planes to fill (Z=0, Z=1, Z=2)
    
    println!("Generating 3D Ulam structure for size {}x{}x{}...", n, n, max_z);

    let (spiral_grid, max_num) = generate_3d_projection(n, max_z);
    
    print_projection(&spiral_grid, max_num, n, max_z);
}

https://play.rust-lang.org/?version=stable&mode=debug&edition=2024&gist=f098441936b2deca12f61ab59e9a759e