Self-made.

ترخيص

I made this with SAGE, an open-source math package. The latest source code lives here, and has a few better variable names & at least one small bug fix than the below. Others have requested source code for images I generated, below. Code is en:GPL; the exact code used to generate this image follows:

#*****************************************************************************
#       Copyright (C) 2008 Dean Moore  < dean dot moore at deanlm dot com >
#                                      < deanlorenmoore@gmail.com >           
#                                        
#
#  Distributed under the terms of the GNU General Public License (GPL)
#                  http://www.gnu.org/licenses/
#*****************************************************************************
#################################################################################
#                                                                               #
# Animated Sierpinski Triangle.                                                 #
#                                                                               #
# Source code written by Dean Moore, March, 2008, open source GPL (above),      #
# source code open to the universe.                                             #
#                                                                               #
# Code animates construction of a Sierpinski Triangle.                          #
#                                                                               #
# See any reference on the Sierpinski Triangle, e.g., Wikipedia at              #
# < http://en.wikipedia.org/wiki/Sierpinski_triangle >; countless others are    #
# out there.                                                                    #
#                                                                               #
#                              Other info:                                      #
#                                                                               #
# Written in sage mathematical package sage (http://www.sagemath.org/), hence   #
# heavily using computer language Python (http://www.python.org/).              #
#                                                                               #
# Important algorithm note:                                                     #
#                                                                               #
# This code does not use recursion.                                             #
#                                                                               #
# More topmatter & documentation probably irrelevant to most:                   #
#                                                                               #
# Inspiration: I viewed it an interesting problem, to try to do an animated     #
# construction of a Sierpinski Triangle in sage.  Thought I'd be lazy & search  #
# the 'Net for open-source versions of this I could simply convert to sage, but #
# the open-source code I found was poorly documented & I couldn't figure it     #
# out, so I gave up & solved the problem from scratch.                          #
#                                                                               #
# Also, I wanted to animate the construction, which I did not find in           #
# open-source code on the 'Net.                                                 #
#                                                                               #
# Comments on algorithm:                                                        #
#                                                                               #
# The code I found on the 'Net was recursive.  I do not much like recursion,    #
# considering it way for programmers to say, "Look how smart I am!  I'm using   #
# recursion!  Aren't I cool?!"  I feel strongly recursion is often confusing,   #
# can chew up too much memory, and should be avoided except when                #
#                                                                               #
# a) It's unavoidable, or                                                       #
# b) The code would be atrocious without it.                                    #
#                                                                               #
# Did some thinking & swearing, but concocted a non-recursive method, and by    #
# doing the problem from scratch.  Guess it avoids all charges of copyright     #
# violation, plagiarism, whatever.                                              #
#                                                                               #
# More on algorithm via ASCII art.  Below we have a given triangle, shaded via  #
# x's.                                                                          #
#                                                                               #
# The next "generation" is the blank triangles.  Sit down & start a Sierpinski  #
# Triangle on scratch: the next generation is always two on each side of a      #
# given triangle from the last generation, one on top.  Algorithm takes the     #
# given, shaded triangle (below), and makes the three of the next generation    #
# arising from it.                                                              #
#                                                                               #
# See code for more on how this works.                                          #
#                            __________                                         #
#                            \        /                                         #
#                             \      /                                          #
#                              \    /                                           #
#                               \  /                                            #
#                       _________\/_________                                    #
#                       \ xxxxxxxxxxxxxxxx /                                    #
#                        \ xxxxxxxxxxxxxx /                                     #
#                         \ xxxxxxxxxxxx /                                      #
#                          \ xxxxxxxxxx /                                       #
#                  _________\ xxxxxxxx /_________                               #
#                  \        /\ xxxxxx /\        /                               #
#                   \      /  \ xxxx /  \      /                                #
#                    \    /    \ xx /    \    /                                 #
#                     \  /      \  /      \  /                                  #
#                      \/        \/        \/                                   #
#                                                                               #
#################################################################################
#                                                                               #
# Begin program:                                                                #
#                                                                               #
# First we need three functions; see the below code on how they are used.       #
#                                                                               #
# The three functions *right_side_triangle* , *left_side_triangle* &            #
# *top_triangle* are here defined & not as "lambda" functions, as they need     #
# documented.                                                                   #
#                                                                               #
# I don't care to replicate the poorly-documented code I found on the 'Net.     #
#                                                                               #
#################################################################################
#                                                                               #
# First function, *right_side_triangle*.                                        #
#                                                                               #
# Function *right_side_triangle* gives coordinates of next triangle on right    #
# side of a given triangle whose coordinates are passed in.                     #
#                                                                               #
# Points *p*, *r*, *q*, *s* & *t* are labeled as passed in:                     #
#                                                                               #
#  (p, r)____________________(q, r)                                             #
#        \                  /                                                   #
#         \                /                                                    #
#          \              /                                                     #
#           \            /                                                      #
#            \  (p1, r1)/_________ (q1, r1)                                     #
#             \        /\        /                                              #
#              \      /  \      /                                               #
#               \    /    \    /                                                #
#                \  /      \  /                                                 #
#                 \/        \/                                                  #
#               (s, t)   (s1, t1)                                               #
#                                                                               #
# p1 = (q + s)/2, a simple average.                                             #
# q1 = q + (q - s)/2 = (3*q - s)/2                                              #
# r1 = (r + t)/2, a simple average.                                             #
# s1 = q, easy.                                                                 #
# t1 = t, easy.                                                                 #
#                                                                               #
#################################################################################   

def right_side_triangle(p,q,r,s,t):

    p1 = (q + s)/2
    q1 = (3*q - s)/2
    r1 = (r + t)/2
    s1 = q        # A placeholder, solely to make code clear.
    t1 = t        # Ditto, a placeholder.  

    return ((p1,r1),(q1, r1),(s1, t1))

# End of function *right_side_triangle*.

#################################################################################
#                                                                               #
# Function *left_side_triangle*:                                                #
#                                                                               #
#                (p, q) ____________________(q, r)                              #
#                       \                  /                                    #
#                        \                /                                     #
#                         \              /                                      #
#                          \            /                                       #
#         (p1, r1) _________\ (q1, r1) /                                        #
#                  \        /\        /                                         #
#                   \      /  \      /                                          #
#                    \    /    \    /                                           #
#                     \  /      \  /                                            #
#                      \/        \/                                             #
#                   (s1, t1)   (s, t)                                           #
#                                                                               #
# p1 = p - (s - p)/2 = (2p-s+p)/2 = (3p - s)/2                                  #
# q1 = (p + s)/2, a simple average                                              #
# r1 = (r + t)/2, a simple average.                                             #
# s1 = p, easy.                                                                 #
# t1 = t, easy.                                                                 #
#                                                                               #
################################################################################# 

def left_side_triangle(p,q,r,s,t): 
 
    p1 = (3*p - s)/2
    q1 = (p + s)/2
    r1 = (r + t)/2
    s1 = p        # A placeholder, solely to make code clear.
    t1 = t        # Ditto, a placeholder.
    
    return ((p1,r1),(q1, r1),(s1, t1))

# End of function *left_side_triangle*.  

#################################################################################
#                                                                               #
# Function *top_triangle*.                                                      #
#                                                                               #
#                   (p1, r1) __________ (q1, r1)                                #
#                            \        /                                         #
#                             \      /                                          #
#                              \    /                                           #
#                               \  / (s1, t1)                                   #
#                 (p, r)_________\/_________                                    #
#                       \ xxxxxxxxxxxxxxxx /                                    #
#                        \ xxxxxxxxxxxxxx / (q, r)                              #
#                         \ xxxxxxxxxxxx /                                      #
#                          \ xxxxxxxxxx /                                       #
#                           \ xxxxxxxx /                                        #
#                            \ xxxxxx /                                         #
#                             \ xxxx /                                          #
#                              \ xx /                                           #
#                               \  /                                            #
#                                \/                                             #
#                              (s, t)                                           #
#                                                                               #
# p1 = (p + s)/2, a simple average.                                             #
# q1 = (s + q)/2, a simple average                                              #
# r1 = r + (r - t)/2 = (3r - t)/2                                               #
# s1 = s, easy.                                                                 #
# t1 = r, easy.                                                                 #
#                                                                               #
#################################################################################

def top_triangle(p,q,r,s,t): 

    p1 = (p + s)/2
    q1 = (s + q)/2
    r1 = (3*r - t)/2
    s1 = s          # Again, both this & next are
    t1 = r          # placeholders, solely to make code clear.

    return ((p1,r1),(q1, r1),(s1, t1))

# End of function *top_triangle*. 

#################################################################################
#                                                                               #
# Main program commences:                                                       #
#                                                                               #
################################################################################# 

# Top matter a user may wish to vary:

number_of_generations   = 8       # How "deep" goes the animation after initial triangle.
first_triangle_color    = (1,0,0) # First triangle's rgb color as red-green-blue tuple.
chopped_piece_color     = (0,0,0) # Color of "chopped" pieces as rgb tuple.
delay_between_frames    = 50      # Time between "frames" of final "movie."
figure_size             = 12      # Regulates size of final image.
initial_edge_length     = 3^7     # Initial edge length. 

# End of material user may realistically vary.  Rest should churn without user input.

number_of_triangles_in_last_generation = 3^number_of_generations # Always a power of three.
images                                 = []                      # Holds images of final "movie."  
coordinates                            = []                      # Holds coordinates. 

p0 = (0,0)                                # Initial points to start iteration -- note
p1 = (initial_edge_length, 0)             # y-values of *p0* & *p1* are the same -- an
p2 = ((p0[0] + p1[0])/2,                  # important book-keeping device.
     ((initial_edge_length/2)*sin(pi/3))) # Equilateral triangle; see any Internet
                                          # reference on these.

# We make a polygon (triangle) of initial points:

this_generations_image = polygon((p0, p1, p2), rgbcolor=first_triangle_color) 

images.append(this_generations_image) # Save image from last line.

coordinates = [( ( (p0[0] + p2[0])/2, (p0[1] + p2[1])/2 ),   # Coordinates
                 ( (p1[0] + p2[0])/2, (p1[1] + p2[1])/2 ),   # of second
                 ( (p0[0] + p1[0])/2, (p0[1] + p1[1])/2 ) )] # triangle.
                                                             # It is *supremely* important
                                                             # that the y-values of the first two
                                                             # points are equal -- check definitions
                                                             # above & code below.

this_generations_image = polygon(coordinates[0],             # Image of second triangle.
                                 rgbcolor=chopped_piece_color)

images.append(images[0] + this_generations_image) # Save second image, tacked on top of first.

# Now the loop that makes the images: 

number_of_triangles_in_this_generation = 1 # We have made one "chopped" triangle, the second, above.

while number_of_triangles_in_this_generation < number_of_triangles_in_last_generation:

    this_generations_image       = Graphics() # Holds next generation's image, initialize.
    next_generations_coordinates = []         # Holds next generation's coordinates, set to null. 

    for a,b,c in coordinates: # Loop on all triangles.

        (p, r)  = a      # Right point; note y-value of this & next are equal.
        (q, r1) = b      # Left point; note r1 = r & thus *r1* is irrelevant;
                         # it's only there for book-keeping.
        (s, t)  = c      # Bottom point.

        # Now construct the three triangles & their three polygons of the next
        # generation.

        right_triangle = right_side_triangle(p,q,r,s,t) # Here use those
        left_triangle  = left_side_triangle (p,q,r,s,t) # utility functions
        upper_triangle = top_triangle       (p,q,r,s,t) # defined at top.

        right = polygon(right_triangle, rgbcolor=(chopped_piece_color)) # Make next
        left  = polygon(left_triangle,  rgbcolor=(chopped_piece_color)) # generation's
        top   = polygon(upper_triangle, rgbcolor=(chopped_piece_color)) # triangles.

        this_generations_image = this_generations_image + (right + left + top) # Add image.
        
        next_generations_coordinates.append(right_triangle) # Save the coordinates
        next_generations_coordinates.append( left_triangle) # of triangles of the
        next_generations_coordinates.append(upper_triangle) # next generation.

       # End of "for a,b,c" loop.

    coordinates = next_generations_coordinates         # Save for next generation.
    images.append(images[-1] + this_generations_image) # Make next image: all previous
                                                       # images plus latest on top.
    number_of_triangles_in_this_generation *= 3        # Bump up.
 
# End of *while* loop.

a = animate(images, figsize=[figure_size, figure_size], axes=False) # Make image, ...
a.show(delay = delay_between_frames)                                # Show image.
 
 # End of program.