>>> print_triangle(get_sierpinski(5)) /\ /__\ /\ /\ /__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\ /\ /\ /__\ /__\ /\ /\ /\ /\ /__\/__\ /__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\ /__\/__\/__\/__\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\ /__\/__\ /__\/__\ /__\/__\ /\ /\ /\ /\ /\ /\ /\ /\ /__\ /__\ /__\ /__\ /__\ /__\ /__\ /__\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /\ /__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\/__\ # under mit license #! /usr/bin/env python # # N = 4: # /\ # /__\ # /\ /\ # /__\/__\ # /\ /\ # /__\ / \ # /\ /\ /\ /\ # /__\/__\/__\/__\ # /\ /\ # /__\ /__\ # /\ /\ /\ /\ # /__\/__\ /__\/__\ # /\ /\ /\ /\ # /__\ / \ /__\ /__\ # /\ /\ /\ /\ /\ /\ /\ /\ # /__\/__\/__\/__\/__\/__\/__\/__\ # # N = 3: # /\ # /__\ # /\ /\ # /__\/__\ # /\ /\ # /__\ /__\ # /\ /\ /\ /\ # /__\/__\/__\/__\ # # N = 2: # /\ # /__\ # /\ /\ # /__\/__\ # # N = 1: # /\ # /__\ # # N = 0: (trivial case) # import sys # returns a list of lines where # each line contains a 2-element list: # a character and a position def get_sierpinski(n): assert n >= 0 if n == 0: return [] if n == 1: return [[['/', 1], ['\\', 2]], # /\ [['/', 0], ['_', 1], ['_', 2], ['\\', 3]]] # /__\ # ok, a bit more complicated: # let's assemble top part and the bottom parts seperately # check out the N=4 example above # there are 3 big triangles: the top one sits on the "spikes" # of the bottom two. # but those 3 triangles are made of 3 smaller triangles, # where the top of the small triangle sits on the bottom # 2, and so on... top, bottom = [], [] for line in get_sierpinski(n-1): t, bl, br = [], [], [] for (character, start) in line: t.append([character, start+2**(n-1)]) bl.append([character, start]) # left triangle br.append([character, start+2**n]) # right triangle top.append(t) bottom.append(bl + br) return top + bottom def print_triangle(triangle): for line in triangle: current_column = 0 for (character, start) in line: while current_column != start: sys.stdout.write(" ") current_column += 1 sys.stdout.write(character) current_column += 1 sys.stdout.write("\n") if __name__ == "__main__": size = 3 if sys.argv[1:]: size = int(sys.argv[1]) print_triangle(get_sierpinski(size))

## 10 October 2006

### Sierpinski — in ASCII, in Python

I wrote this in the fall of 2004 (I was taking a class with one of the best teachers I've ever had and she gave this as a bonus on an exam — this fractal was on her t-shirt and she asked its name).
(this works under python 2.4)