Different Pascal's triangle implementation

Patterns/pascals_triangle.py

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+from math import factorial
+from itertools import combinations
+
+#This is a recursive implementation for generating Pascal's triangle.
+def recursive(n):
+	def recursive_row(n,k):
+		if k == 0 or k == n:
+			return 1
+		return recursive_row(n-1, k-1) + recursive_row(n-1, k);
+	triangle = [];
+	for row in range(n):
+		curr_row = [];
+		for k in range(row+1):
+			curr_row.append(recursive_row(row, k))
+		triangle.append(curr_row)	
+
+	return triangle
+
+#This is the typical definition of Pascal's triangle.
+def bruteForce_sumLast(n):
+	triangle = []
+	for row in range(n):
+		curr_row = []
+		for i in range(row+1):
+			if i == 0 or i == row:
+				curr_row.append(1);
+			else:
+				curr_row.append(triangle[-1][i-1]+triangle[-1][i])
+		triangle.append(curr_row)
+	return triangle
+
+#We define the n choose k function: https://en.wikipedia.org/wiki/Combination
+#This will be useful in the next function.
+def nchoosek(n,k):
+	#There are multiple ways of computing this aswell!
+	#For example, it can be computed recursively or via the definition nCk = n!/(k!*(n-k)!)
+	return len(list(combinations(range(n),k)))
+
+#This is the definition of the Pascal's triangle using combinatorial numbers.
+def bruteForce_factorial(n):
+	triangle = []
+	for row in range(n):
+		curr_row = []
+		for col in range(row+1):
+			curr_row.append( nchoosek(row, col) )
+		triangle.append(curr_row)
+	return triangle
+
+
+#This algorithm is taken from user MortalViews in StackExchange from the post 
+#https://stackoverflow.com/questions/24093387/pascals-triangle-for-python
+#This is just for visualization purposes!
+#Just enter the output of any of the above functions and it will work.
+def draw_beautiful(ps):
+    max = len(' '.join(map(str,ps[-1])))
+    for p in ps:
+        print(' '.join(map(str,p)).center(max)+'\n')

Patterns/sierpinskys_triangle.py

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+import matplotlib.pylab as plt
+from random import randint
+
+def midpoint(p1, p2):
+	return ((p1[0]+p2[0])/2, (p1[1]+p2[1])/2)
+
+width, height = 1, 1
+p, q, r = (width/2, height), (0, 0), (width, 0); #This three points form a triangle
+triangle = [p,q,r]
+mid_point = (width/2, height/2)
+
+for _ in range(5000): #if you increase this number, then the fractal will be more defined!
+	mid_point = midpoint(mid_point, triangle[randint(0,2)])
+	plt.plot(mid_point[0], mid_point[1], 'm.', markersize=2)
+plt.show()