Nested Circle of Squares (Source Code)

Knowing how to draw circle of squares, draw the following nested circle of squares with either recursion or iteration.

Source Code:

import turtle
import math
screen = turtle.Screen()
screen.title('Nested Squares Circles - PythonTurtle.Academy')
screen.setup(1000,1000)
screen.setworldcoordinates(-1000,-1000,1000,1000)
turtle.speed(0)
turtle.hideturtle()
screen.tracer(0,0)

def draw_square(x,y,length,direction,color):
    turtle.up()
    turtle.goto(x-length/(2**0.5)*math.cos(math.radians(direction+45)),y-length/(2**0.5)*math.sin(math.radians(direction+45)))
    turtle.seth(direction)
    turtle.color(color)
    turtle.down()
    for _ in range(4):
        turtle.fd(length)
        turtle.left(90)

def draw_square_circle(radius,direction,n):
    length = 2*radius*math.sin(math.radians(180/n))
    length = length/(2**0.5)
    for _ in range(n):
        draw_square(radius*math.cos(math.radians(180/n))*math.cos(math.radians(direction)),\
                    radius*math.cos(math.radians(180/n))*math.sin(math.radians(direction)),\
                    length, direction+45,'black')
        direction += 360/n

def draw_square_circle_recursive(radius,direction,n):
    if radius < 10: return
    draw_square_circle(radius,direction,n)
    r = radius*math.cos(math.radians(180/n))-radius*math.sin(math.radians(180/n))
    draw_square_circle_recursive(r,direction+180/n,n)
    
draw_square_circle_recursive(600,0,11)
screen.update()