Question

Using python

Here is the code

import turtle

def draw_triangle(vertex, length, k):

'''

Draw a triangle at depth k given the bottom vertex.

  

vertex: a tuple (x,y) that gives the coordinates of the bottom vertex.

When k=0, vertex is the left bottom vertex for the outside triangle.

length: the length of the original outside triangle (the biggest one).

k: the depth of the input triangle.

As k increases by 1, the triangles shrink to a smaller size.

When k=0, the function will draw the outside triangle.

'''

t.up()

t.goto(vertex)

if k > 0:

t.setheading(60)

t.down()

for i in range(3):

t.forward(length/2**k)

t.left(120)

return(None)

def new_vertex(vertex, length, k):

'''

Find the the bottom vertexes of three surrounding triangles at depth k+1

for the triangle at depth k with the bottom vertex.

  

vertex: a tuple (x,y) that gives the coordinates of the bottom vertex.

When k=0, vertex is the left bottom vertex for the outside triangle.

length: the length of the original outside triangle (the biggest one).

k: the depth of the input triangle.

As k increases by 1, the triangles shrink to a smaller size.

'''

if k==0:

return([(vertex[0]+length/2,vertex[1])])

x = vertex[0]

y = vertex[1]

x1 = x

y1 = y + length/2**(k+1)*(3**0.5)

x2 = x - length/2**(k+1)

y2 = y

x3 = x + length/2**(k+1)

y3 = y

return([(x1,y1),(x2,y2),(x3,y3)])

win = turtle.Screen()

win.setworldcoordinates(-10,-10,110,100)

t = turtle.Turtle(visible=False)

t.speed(2000)

sideLen = 100

draw_triangle((0,0),sideLen,0)

print(new_vertex((0,0),sideLen,0))

draw_triangle((sideLen/2,0),sideLen,1)

print(new_vertex((sideLen/2,0),sideLen,1))

draw_triangle((sideLen/4,0),sideLen,2)

print(new_vertex((sideLen/4,0),sideLen,2))

  

win.exitonclick()

(5 points) Complete the following code to create a Sierpinski triangle with n levels, where n is a positive integer indicating the max depth of triangles in the Sierpinski triangle. You can modify the code if needed. import turtle

Answer 1

from turtle import *
size=800
min=64
pytho=0.8660255 # Pytho = squareroot of 3/2

def triangle(l,x,y):
if l > min:   
l=l/2   
triangle(l,x,y)
triangle(l,x+l,y)
triangle(l,x+l/2,y+l*pytho)   
else:   
goto(x,y); pendown()
begin_fill()
forward(l); left(120)   
forward(l); left(120)
forward(l)
end_fill()
setheading(0)   
penup(); goto(x,y)

penup()
speed('fastest')
triangle(size,-size/2,-size*pytho/2.0)
done()
# code is using recursion