# Draw a Golden Dragon Curve in Python Using Turtle

## Python Program to Draw a Golden Dragon Curve Using Turtle

```# Python Program to Draw a golden dragon curve using turtle

# import turtle and math
import turtle
import math

screen = turtle.Screen()
screen.setup(1000,1000)
screen.setworldcoordinates(-1000,-1000,1000,1000)
turtle.speed(0)
turtle.hideturtle()
turtle.pencolor('gold')
screen.bgcolor('royal blue')
screen.tracer(0,0)

# calculate golden ratio
golden_ratio = (1+5**0.5)/2
r1 = r = (1/golden_ratio)**(1/golden_ratio)
r2 = r1**2
angle1 = math.acos((1+r**2-r**4)/(2*r))
angle2 = math.acos((1+r**4-r**2)/(2*r**2))
print(r1,r2,math.degrees(angle1),math.degrees(angle2))

def golden_dragon(x1,y1,x2,y2,turn,n):
dist = ((x2-x1)**2 + (y2-y1)**2)**0.5
if dist<1:
turtle.goto(x2,y2)
return
angle = math.atan2(y2-y1,x2-x1)
if turn:
px = x1+dist*r1*math.cos(angle+angle1)
py = y1+dist*r1*math.sin(angle+angle1)
else:
px = x1+dist*r2*math.cos(angle-angle2)
py = y1+dist*r2*math.sin(angle-angle2)
golden_dragon(x1,y1,px,py,True,n-1)
golden_dragon(px,py,x2,y2,False,n-1)

turtle.up()
turtle.goto(-500,-200)
turtle.down()
golden_dragon(-500,-200,700,-200,True,3)
screen.update()```