# Tk_Random_Island.py

# Tk_Random_Island.py

from Tkinter import *
from PIL import Image, ImageTk
import random
import math
import time
ww = 600
hh = 600
ww2 = ww/2
hh2 = hh/2

root = Tk()
root.title("Tk Random Island")
root.geometry("%dx%d+-10+0"%(ww,hh))
canvas = Canvas(root, width=ww, height=hh, bg='royal blue')
canvas.pack()

def draw_line(x1,y1,x2,y2): # function to draw line
    xy.append((ww2+x2,hh2+y2))

def dist(p1,p2): # Euclidean distance betwen p1 and p2
    return ((p1[0]-p2[0])**2 + (p1[1]-p2[1])**2)**0.5

def shoreline(x1,y1,x2,y2,ratio): # recurisve function to draw the shoreline
    L = dist((x1,y1),(x2,y2))
    if L <= 1: # distance is short enough, directly draw the line
        draw_line(x1,y1,x2,y2)
        return
    rs = ratio + random.uniform(-0.1,0.1) # let ratio flucuate slightly around the chosen value
    rs = max(0.5,rs) # make sure ratio stays at least half of the length
    midx = (x1+x2)/2 # center of ellipse
    midy = (y1+y2)/2
    rx = L/2 + (2*rs-1)/2*L # width of ellipse
    ry = ((L*rs)**2 - (L/2)**2)**0.5 # height of ellipse
    theta = math.atan2(y2-y1,x2-x1) # the tilt angle of ellipse
    alpha = random.uniform(math.pi*0.3,math.pi*0.7) # flucuate around math.pi/2
    x3 = rx*math.cos(alpha)*math.cos(theta) - ry*math.sin(alpha)*math.sin(theta) + midx # parametric equation for ellipse
    y3 = rx*math.cos(alpha)*math.sin(theta) + ry*math.sin(alpha)*math.cos(theta) + midy
    shoreline(x1,y1,x3,y3,ratio) # do this recursively on each segment
    shoreline(x3,y3,x2,y2,ratio)

while 1:
    xy = []
    canvas.delete('all')
    shoreline(-200,0,200,0,0.55) # call recursion
    shoreline(200,0,-200,0,0.55) # call recursion

    canvas.create_polygon(xy, fill="forest green", outline="tan", width=5)
    canvas.update()