Generates pascal triangle image

pascal.py

import random

from PIL import Image
import matplotlib.colors as colors

from python.less2.combinatorics import vartiations

'''
'   Calculates combination number using cache (doesn't recalculate already calculated values)
'''


def comb_number(n, k, cache=None):
    if k == 0 or k == n:
        return 1
    if cache is None:
        cache = [[0 for _ in range(k)] for _ in range(n)]
    if cache[n - 1][k - 1] == 0:
        cache[n - 1][k - 1] = comb_number(n - 1, k - 1, cache) + comb_number(n - 1, k, cache)
    return cache[n - 1][k - 1]


'''
'   Calculates combination number inefficiently
'''


def comb_number2(n, k):
    if k == 0 or k == n:
        return 1
    else:
        return comb_number2(n - 1, k - 1) + comb_number2(n - 1, k)


'''
'   Calculates the numbers in pascal triangle
'   Returns list of list with numbers each list represents one row in the pascal triangle
'''


def hex_to_rgb(value):
    value = value.lstrip('#')
    lv = len(value)
    return tuple(int(value[i:i + lv // 3], 16) for i in range(0, lv, lv // 3))


def rgb_to_hex(rgb):
    return '#%02x%02x%02x' % rgb


def pascal(n):
    cache = [[0 for _ in range(n)] for _ in range(n)]
    numbers = []
    for i in range(0, n):
        line = []
        for j in range(0, i + 1):
            line.insert(0, comb_number(i, j, cache))
        numbers.insert(0, line)
    return numbers


def draw_pascal(n, d, input_scale=1):
    pascal_list = pascal(n)

    if input_scale % 2 == 1:
        direction_base = range(0, input_scale)
    else:
        direction_base = range(0, input_scale + 1)

    # [0, 2], [2, 2], [2, 0], [2, 1], [1,2]]
    directions = vartiations(direction_base, 2, True)
    scale = len(direction_base)
    width = n * scale
    height = n * scale
    im = Image.new("RGB", (width + 1, height + 2))

    color_map = []
    list_colors = list(colors.cnames.items())
    random.shuffle(list_colors)
    for i in range(d):
        color_map.insert(i, list_colors[431 * i * d % len(colors.cnames)])

    for i in range(len(pascal_list)):
        offset = int((n - len(pascal_list[i])) * scale / 2)
        for j in range(len(pascal_list[i])):
            for pix in directions:
                (x, y) = (
                    (offset + j * scale + pix[0]), height - (scale * i + pix[1]))
                im.putpixel(
                    (x, y), hex_to_rgb(color_map[pascal_list[i][j] % d][1]))

    im.show()


draw_pascal(30, 5, 20)