http://www.engare.design/

engare.py

import math
import turtle

def rotate(a, v):
    (x, y)= v
    return (math.cos(a)*x - math.sin(a)*y, math.sin(a)*x + math.cos(a)*y)

def demo0(n):
    angle_step= 2*math.pi/n
    p= (0,100)
    turtle.up()
    for i in range(n+1):
        turtle.goto(p)
        p= rotate(angle_step, p)
        turtle.down()
#TODO spirals !
#demo0(5)
#demo0(int(turtle.numinput("rotations", "combien de côtés ?")))

def add(v0, v1):
    (x0, y0)=v0
    (x1, y1)=v1
    return (x0+x1, y0+y1)

def mult_scalar(k, v):
    (x, y)= v
    return (k*x, k*y)

def sub(v0, v1):
    return add(v0, mult_scalar(-1, v1))

def rotate_around(c, a, v):
    return add(c, rotate(a, sub(v, c)))

def demo1_helper(c, p, n):
    turtle.up()
    for i in range(n+1):
        turtle.goto(p)
        p= rotate_around(c, 2*math.pi/n, p)
        turtle.down()

def demo1(n):
    demo1_helper((50, 25), (0,100), n)

#demo1(int(turtle.numinput("rotations", "combien de côtés ?")))

def demo2(n0, n1):
    p= (0, 100)
    c= (0, 50)
    for i in range(n0):
        demo1_helper(c, p, n1)
        c= rotate(2*math.pi/n0, c)

#demo2(int(turtle.numinput("rotations", "combien de polygones ?")), int(turtle.numinput("rotations", "combien de côtés ?")))

def demo3(r0, r1):
    p0= (0, r0)
    p1= (0, r0+r1)
    n= 512
    a_step= 2*math.pi/n
    i_range=range(n)
    turtle.up()
    for i0 in i_range:
        p1= rotate_around(p0, a_step*-3, p1)
        turtle.goto(p1)
        turtle.down()
        p0= rotate(a_step, p0)

#demo3(50, -45)

def three_arms(rv0, rv1, rv2):
    (r0, v0)= rv0
    (r1, v1)= rv1
    (r2, v2)= rv2
    p0= (0, r0)
    p1= (0, r0+r1)
    p2= (0, r0+r1+r2)
    n= 512
    a_step= 2*math.pi/n
    a=0
    turtle.up()
    for i0 in range(n):
        turtle.goto(rotate(a*v0, rotate_around(p0, a*v1, rotate_around(p1, a*v2, p2))))
        turtle.down()
        a+= a_step

def demo4(size):
    #size = L + M + S
    # S= L/6
    # M= L/2
    l= size/(1+1/2+1/6)
    three_arms((l,1), (l/2,4), (l/6,16))


def demo5(size, n):
    c= size*15/200 # n =10
    # c= size*4/200 # n= 8
    # c= size*10/200 # n= 9
    # c= size*25/200 # n= 20
    # size= L + M + S
    # L= M+S+C
    # 2*size= 2*L + C
    l=(size+c)/2
    m_size= 1 + math.sqrt(2)/2
    s_size= (2-math.sqrt(2))/4
    m_s_ratio= m_size/s_size
    # size- L = M (1+S/M)
    m= (size - l)/(1+s_size/m_size)
    s= (m/ m_size) * s_size
    three_arms((l,1),(m,-n),(s, 4*n))

def demo6(size):
    # size= L + M + S = 3*M + 2*S=(3+1/3)M
    # L= 2*M + S
    # S=M/6
    m= size/(3+1/3)
    s= m/6
    three_arms((2*m+s,1), (m,-12), (s, 12*6))

#demo5(200, 10)
#demo4(300)
demo6(200)

# 11/12 * 2 * math.pi
turtle.exitonclick()