Task: Kronecker product based fractals


C++: #include <cassert>
#include <vector>

#include <QImage>

template <typename scalar_type> class matrix {
public:
    matrix(size_t rows, size_t columns)
        : rows_(rows), columns_(columns), elements_(rows * columns) {}
    matrix(size_t rows, size_t columns,
        const std::initializer_list<std::initializer_list<scalar_type>>& values)
        : rows_(rows), columns_(columns), elements_(rows * columns) {
        assert(values.size() <= rows_);
        size_t i = 0;
        for (const auto& row : values) {
            assert(row.size() <= columns_);
            std::copy(begin(row), end(row), &elements_[i]);
            i += columns_;
        }
    }
    size_t rows() const { return rows_; }
    size_t columns() const { return columns_; }

    const scalar_type& operator()(size_t row, size_t column) const {
        assert(row < rows_);
        assert(column < columns_);
        return elements_[row * columns_ + column];
    }
    scalar_type& operator()(size_t row, size_t column) {
        assert(row < rows_);
        assert(column < columns_);
        return elements_[row * columns_ + column];
    }
private:
    size_t rows_;
    size_t columns_;
    std::vector<scalar_type> elements_;
};


template <typename scalar_type>
matrix<scalar_type> kronecker_product(const matrix<scalar_type>& a,
                                      const matrix<scalar_type>& b) {
    size_t arows = a.rows();
    size_t acolumns = a.columns();
    size_t brows = b.rows();
    size_t bcolumns = b.columns();
    matrix<scalar_type> c(arows * brows, acolumns * bcolumns);
    for (size_t i = 0; i < arows; ++i)
        for (size_t j = 0; j < acolumns; ++j)
            for (size_t k = 0; k < brows; ++k)
                for (size_t l = 0; l < bcolumns; ++l)
                    c(i*brows + k, j*bcolumns + l) = a(i, j) * b(k, l);
    return c;
}

bool kronecker_fractal(const char* fileName, const matrix<unsigned char>& m, int order) {
    matrix<unsigned char> result = m;
    for (int i = 0; i < order; ++i)
        result = kronecker_product(result, m);

    size_t height = result.rows();
    size_t width = result.columns();
    size_t bytesPerLine = 4 * ((width + 3)/4);
    std::vector<uchar> imageData(bytesPerLine * height);

    for (size_t i = 0; i < height; ++i)
        for (size_t j = 0; j < width; ++j)
            imageData[i * bytesPerLine + j] = result(i, j);

    QImage image(&imageData[0], width, height, bytesPerLine, QImage::Format_Indexed8);
    QVector<QRgb> colours(2);
    colours[0] = qRgb(0, 0, 0);
    colours[1] = qRgb(255, 255, 255);
    image.setColorTable(colours);
    return image.save(fileName);
}

int main() {
    matrix<unsigned char> matrix1(3, 3, {{0,1,0}, {1,1,1}, {0,1,0}});
    matrix<unsigned char> matrix2(3, 3, {{1,1,1}, {1,0,1}, {1,1,1}});
    matrix<unsigned char> matrix3(2, 2, {{1,1}, {0,1}});
    kronecker_fractal("vicsek.png", matrix1, 5);
    kronecker_fractal("sierpinski_carpet.png", matrix2, 5);
    kronecker_fractal("sierpinski_triangle.png", matrix3, 8);
    return 0;
}






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)