maximum likelihood

from PIL import Image, ImageDraw, ImageFont

import math



# Load the image

img_path = './musta aukko.jpg'

image = Image.open(img_path)

# Constants for the equations

equations = [

    "c^2 = a^2 + b^2",

    "E = mc^2",

    "F = G \\frac{m_1 m_2}{r^2}",

    "\\frac{d^2r}{dt^2} = -\\frac{GM}{r^2}",

    "S = \\pi r^2",

    "\\Psi(r,\\theta,\\phi) = R(r)\\Theta(\\theta)\\Phi(\\phi)"

]



# Define the draw object

draw = ImageDraw.Draw(image)



# Function to calculate the position of the text

def get_text_position(angle, radius, image_size):

    x = int(image_size[0]/2 + radius * math.cos(angle))

    y = int(image_size[1]/2 + radius * math.sin(angle))

    return x, y



# Font size and type

font_size = 20

font = ImageFont.truetype("arial.ttf", font_size)



# Angle and radius

start_angle = 10

angle_step = 1  # radians

radius_step = 1.0  # pixels per step

radius = 5



# Draw the equations spiraling outwards

for equation in equations:

    angle = start_angle

    while radius < min(image.size)/2:

        x, y = get_text_position(angle, radius, image.size)

        draw.text((x, y), equation, font=font, fill=(255,255,255,255))

        angle += angle_step

        radius += radius_step

    radius += 20  # Increase initial radius for the next equation



# Save the modified image

modified_img_path = './musta aukko_mod.jpg'
image.save(modified_img_path)
modified_img_path