import turtle
import numpy as np

'''
Function that creates a Sierpinski Triangle
Takes in side and number of times to repeat this pattern
as an argument.
'''
def draw_triangle_up(tobi, angle, side):
    for i in range(0, 3):
        tobi.forward(side)
        tobi.left(angle)

def draw_triangle_down(tobi, angle, side):
    for i in range(0, 3):
        tobi.forward(side)
        tobi.right(angle)


def draw_equilateral_triangle(tobi, side, upside_down):
    if upside_down:
        draw_triangle_down(tobi, 120, side)
    else:
        draw_triangle_up(tobi, 120, side)

def draw_sub_triangles(tobi, start_x, start_y, side, cur_count, num_times):
    if cur_count > num_times:
        return
    else:

        # no drawing while setting the current index
        tobi.penup()
        tobi.setx(start_x)
        tobi.sety(start_y)

        # now put the pen down so we can see what we are drawing
        tobi.pendown()

        draw_equilateral_triangle(tobi, side, True)

        cur_count += 1
        draw_sub_triangles(tobi, (start_x - side/4.0), (start_y - ((np.sqrt(3) * side)) / 4.0), side/2.0, cur_count, num_times)
        draw_sub_triangles(tobi, (start_x + side/4.0), (start_y + ((np.sqrt(3) * side)) / 4.0), side/2.0, cur_count, num_times)
        draw_sub_triangles(tobi, (start_x + 3 * side/4.0), (start_y - ((np.sqrt(3) * side)) / 4.0), side/2.0, cur_count, num_times)


def sierpinski_triangle(side, num_times=1):
    # get turtle screen singleton object
    window = turtle.Screen()
    window.delay(50)

    # instantiate turtle object
    tobi = turtle.Turtle()

    # maintain a list of start points
    start_points = [(tobi.xcor(), tobi.ycor(), side)]

    # maintain current count
    cur_count = 0

    # draw main triangle
    draw_equilateral_triangle(tobi, side, False)


    draw_sub_triangles(tobi, (tobi.xcor() + side/4.0), (tobi.ycor()+ ((np.sqrt(3) * side) / 4.0)), side/2.0, cur_count, num_times)

    window.exitonclick()