# pip install numpy Pillow

import numpy as np
from PIL import Image

def ss(edge0, edge1, x):
    x = (x - edge0) / (edge1 - edge0)
    if x < 0:
        x = 0
    if x > 1:
        x = 1
    return x * x * (3 - 2 * x)

def mmap(x, x0, x1):
    return x * (x1 - x0) + x0

def f(x, y):
    xp = x / width
    yp = y / height

    l = ((0.5 - xp)**2 + (0.5 - yp)**2)**0.5
    l *= 2
    x = l
    res = 0

    # torch
    c0 = 0.15
    c1 = 0.45
    c2 = 0.45
    x0 = 0.9
    x1 = 0.5
    x2 = 0.2

    # flashlight
    c0 = 0.15
    c1 = 0.55
    c2 = 0.35
    x0 = 0.9
    x1 = 0.5
    x2 = 0.25

    res += mmap(ss(x0, 0, x), 0, c0)
    res += mmap(ss(x1, 0, x), 0, c1)
    res += mmap(ss(x2, 0, x), 0, c2)

    return int(255 * res), int(255 * res), int(255 * res)

width, height = 256, 256
image = Image.new("RGB", (width, height))

pixels = []
for y in range(height):
    for x in range(width):
        r, g, b = f(x, y)
        pixels.append((r, g, b))

image.putdata(pixels)

image.save("output_image.png")
print("Image saved as output_image.png")