pascal.py

def main():
    import argparse

    parser = argparse.ArgumentParser(description='Generate Pascal\'s Triangle')
    parser.add_argument('out', help='output file')
    parser.add_argument('--width', '-w', default=1024, help='image width in pixels', type=int)
    parser.add_argument('--modulus', '-m', help='modulus', type=int)
    parser.add_argument('--isosceles', action='store_true', help='render isosceles triangle')
    parser.add_argument('--verbose', '-v', action='count', default=0)
    exgroup = parser.add_mutually_exclusive_group(required=True)
    exgroup.add_argument('--rows', '-r', help='number of rows of Pascal\'s triangle', type=int)
    exgroup.add_argument('--iterates', '-i', help='rows per pixel', type=int)
    args = parser.parse_args()
    n = args.width
    if args.iterates:
        m = args.iterates
    elif args.rows:
        m = (args.rows + args.width - 1) // args.width

    import imageio
    import numpy as np
    p = args.modulus

    arr = np.zeros(n * m + 1, dtype=np.int64)
    arr[0] = 1
    img = np.zeros((n, n + 1), dtype=np.int64)
    for k in range(n):
        img_acc = np.zeros(n * m, dtype=np.int64)
        for j in range(m):
            i = k * m + j
            img_acc += arr[:-1]
            arr[1:i + 2] += arr[:i + 1]
            arr[0] = 1
            arr[i + 1] = 1
            if p:
                arr %= p
        row = np.sum(img_acc.reshape((n, m)), axis=1)[:k + 1]
        if args.isosceles:
            if k % 2 == 0:
                img[k, (n - k) // 2:(n + k + 2) // 2] = row * 2
            else:
                img[k, (n - k) // 2:(n + k + 2) // 2] += row
                img[k, (n - k + 2) // 2:(n + k + 4) // 2] += row
        else:
            img[k, :k + 1] += row
        if args.verbose >= 1:
            print(f'{k/(n-1):2.2%} complete')
    img -= img.min()
    img = img * 255 // np.max(img)
    img = img.astype(np.uint8)

    imageio.imwrite(args.out, img)


if __name__ == '__main__':
    main()