Task: Kronecker product based fractals





Java: package kronecker;


public class ProductFractals {
  
  public static int[][] product(final int[][] a, final int[][] b) {
    
    
    final int[][] c = new int[a.length*b.length][];
    
    
    for (int ix = 0; ix < c.length; ix++) {
      final int num_cols = a[0].length*b[0].length;
      c[ix] = new int[num_cols];
    }
    
    
    for (int ia = 0; ia < a.length; ia++) {
      for (int ja = 0; ja < a[ia].length; ja++) {
        
        for (int ib = 0; ib < b.length; ib++) {
          for (int jb = 0; jb < b[ib].length; jb++) {
             c[b.length*ia+ib][b[ib].length*ja+jb] = a[ia][ja] * b[ib][jb];
          }
        }
      }
    }

    
    return c;
  }

  
  public static void show_matrix(final int[][] m, final char nz, final char z) {
    for (int im = 0; im < m.length; im++) {
      for (int jm = 0; jm < m[im].length; jm++) {
        System.out.print(m[im][jm] == 0 ? z : nz);
      }
      System.out.println();
    }
  }

  
  public static int[][] power(final int[][] m, final int n) {
    
    int[][] m_pow = m;
    
    
    for (int ix = 1; ix < n; ix++) {
      m_pow = product(m, m_pow);
    }
    return m_pow;
  }

  
  private static void test(final int[][] m, final int n) {
    System.out.println("Test matrix");
    show_matrix(m, '*', ' ');
    final int[][] m_pow = power(m, n);
    System.out.println("Matrix power " + n);
    show_matrix(m_pow, '*', ' ');
  }

  
  private static void test1() {
    
    final int[][] m = {{0, 1, 0},
                       {1, 1, 1},
                       {0, 1, 0}};
    
    test(m, 4);
  }

  
  private static void test2() {
    
    final int[][] m = {{1, 1, 1},
                       {1, 0, 1},
                       {1, 1, 1}};
    
    test(m, 4);
  }

  
  private static void test3() {
    
    final int[][] m = {{1, 0, 1},
                       {1, 0, 1},
                       {0, 1, 0}};
    
    test(m, 4);
  }

  
  public static void main(final String[] args) {
    
    test1();
    test2();
    test3();
  }

}



Python: import os
from PIL import Image


def imgsave(path, arr):
    w, h = len(arr), len(arr[0])
    img = Image.new('1', (w, h))
    for x in range(w):
        for y in range(h):
            img.putpixel((x, y), arr[x][y])
    img.save(path)


def get_shape(mat):
    return len(mat), len(mat[0])


def kron(matrix1, matrix2):
    
    final_list = []

    count = len(matrix2)

    for elem1 in matrix1:
        for i in range(count):
            sub_list = []
            for num1 in elem1:
                for num2 in matrix2[i]:
                    sub_list.append(num1 * num2)
            final_list.append(sub_list)

    return final_list


def kronpow(mat):
    
    matrix = mat
    while True:
        yield matrix
        matrix = kron(mat, matrix)


def fractal(name, mat, order=6):
    
    path = os.path.join('fractals', name)
    os.makedirs(path, exist_ok=True)

    fgen = kronpow(mat)
    print(name)
    for i in range(order):
        p = os.path.join(path, f'{i}.jpg')
        print('Calculating n =', i, end='\t', flush=True)

        mat = next(fgen)
        imgsave(p, mat)

        x, y = get_shape(mat)
        print('Saved as', x, 'x', y, 'image', p)


test1 = [
    [0, 1, 0],
    [1, 1, 1],
    [0, 1, 0]
]

test2 = [
    [1, 1, 1],
    [1, 0, 1],
    [1, 1, 1]
]

test3 = [
    [1, 0, 1],
    [0, 1, 0],
    [1, 0, 1]
]

fractal('test1', test1)
fractal('test2', test2)
fractal('test3', test3)