maths-fractal-area

main.py

import math


# This is run recusivly
# s is the length of the squares sides
# x is a counter
def f(s, x):
    if x == 1:  # if x = 1 then
        # return returns the value and quits the function
        return s * s  # Just return the square if we are on the end

    # otherwise

    small_side = math.sqrt((s * s) / 2)
    #                _______
    # small_side = ./ s x s
    #                 -----
    #                   2

    triangle_height = math.sqrt(
        s * s / 4.0 + small_side * small_side)
    #                     _____________________
    # triangle_height = ./ s x s             2
    #                      ----- + small_side
    #                        4

    triangle_area = triangle_height * (s / 2.0)
    #                                    s
    # triangle_area = triangle_height x ---
    #                                    2

    return (s * s) + triangle_area + (f(small_side, x-1) * 2)
    # return s x s + triangle_area + 
    #        then run again but with s = small_side and times the return by 2 
    #         and keep repeating until the end of the branch

# end of function

start = float(input('Starting square: '))
times = int(input('How many times: '))
print 'The area is', f(start, times), 'units squared!'