How to write a recursion syntax for Sierpinski triangle using numpy?

[Bolzano]

Hi,
I'm new to programming in python [total beginner in programming] and I would like to ask you for your help.

So here is my problem:
I'm trying to program a Sierpinski triangle for n-iterations. Here is what I got so far:

import numpy as np
from math import sqrt

#               a       b           c
P = np.array([(0, 0), (1, 0), (1, (1/sqrt(2)))], dtype=float)

# I could start with any point, but decided to start with a
a = np.array((0, 0), dtype=float)

new_point: #1.iteration
#    a   +  b
p1 = P[0] + P[1] new_point #2.iteration
                 t1 = P[0] + p1 
                 t2 = P[1] + p1  
                 t3 = P[2] + p1   
#    b   +  c 
p2 = P[1] + P[2] new_point #2.iteration
                 t4 = P[0] + p2 
                 t5 = P[1] + p2 
                 t6 = P[2] + p2 
#    c   +  a
p3 = P[2] + P[0] new_point #2.iteration
                 t7 = P[0] + p3 
                 t8 = P[1] + p3 
                 t9 = P[2] + p3 

My problem is writing all this in recursion syntax in python (recursion is mandatory).




I even drew everything on the piece of paper, so I understand the algorithm, but don't know how to write it in syntax.

What about plotting all the points? Is there a 'grid' for these arrays? I read about numpy.zeros(), but it was explained this is a function for matrixes, so I'm not sure how to implement this into the program.

Can you help?

[deanhystad]

Why are you using numpy? Seems like it adds nothing to solving this problem.

Can you write code that solves the problem for 1 iteration? I don't think you have the logic correct for that. Once you have the code that computes the three similar triangles the recursion part is simple.

[SheeppOSU]

I would write a function which takes in 3 points for the triangle, makes 3 points for the triangle within it to get 3 sets of 3 points like so: [A, p1, p3], [B, p1, p2], [C, p2, p3]. Then it executes itself with each set of three points. You can figure out what to do with the points and how to tell the program to stop.

Example code: (Code is sorta untested by the way)

import numpy as np
from math import sqrt


def recursive(points):
    p1 = (points[0] + points[1]) / 2
    p2 = (points[1] + points[2]) / 2
    p3 = (points[2] + points[0]) / 2
    for p_set in np.array([points[0], p1, p3], [points[1], p1, p2], [points[2], p3, p2]):
        recursive(p_set)


recursive(np.array([[0, 0], [1, 0], [1, 1/sqrt(2)]]))