sierpiński triangle.py

# coding: utf-8

# In[1]:

#fractal is one of the interesting topics in geometry
#it is usually described by a recursive function
#voila,here we are!
import matplotlib.pyplot as plt


# In[2]:


def sierpiński_triangle(coordinates,lvl,colour='k'):
    
    #stop recursion
    if lvl==0:
        return
    
    #unpack coordinates
    #coordinates have to follow the order of left,mid,right
    left=coordinates[0];mid=coordinates[1];right=coordinates[2]
    
    #compute mid point for each line
    left_new=((mid[0]-left[0])/2+left[0],(mid[1]-left[1])/2+left[1])
    mid_new=((right[0]-left[0])/2+left[0],(right[1]-left[1])/2+left[1])
    right_new=((right[0]-mid[0])/2+mid[0],(mid[1]-right[1])/2+right[1])
    
    #create new coordinates
    coordinates_new=[left_new,mid_new,right_new]
    
    #viz coordinates
    for i in coordinates:
        for j in coordinates:
            if i!=j:            
                plt.plot([i[0],j[0]],[i[1],j[1]],c=colour)    
    
    #recursive plot sub triangles
    sierpiński_triangle([left,left_new,mid_new],lvl-1)
    sierpiński_triangle([left_new,mid,right_new],lvl-1)
    sierpiński_triangle([mid_new,right_new,right],lvl-1)


# In[3]:


sierpiński_triangle([(0,0),(0.5,1),(1,0)],4)


# In[4]:


#you can check turtle version at the following link
# https://runestone.academy/runestone/books/published/pythonds/Recursion/pythondsSierpinskiTriangle.html

#you can check print version at the following link
# https://www.geeksforgeeks.org/sierpinski-triangle/