Fil:Animated construction of Sierpinski Triangle.gif
Hoppa till navigering
Hoppa till sök
Storlek på förhandsvisningen: 581 × 599 pixlar. Andra upplösningar: 233 × 240 pixlar | 465 × 480 pixlar | 950 × 980 pixlar.
Originalfil (950 × 980 pixlar, filstorlek: 375 kbyte, MIME-typ: image/gif, upprepad, 10 bildrutor, 5,0 s)
Sammanfattning
Den här Det diagram skapades med SageMath.
| Beskrivning |
English: Animated construction of Sierpinski Triangle Self-made. LicensieringI 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.
End of code. |
| Datum |
23 mars 2008 (ursprungligt uppladdningsdatum) |
| Källa | Eget arbete (Original text: self-made) |
| Skapare | (Original text: dino (talk)) |
Licensiering
Dino på engelska Wikipedia, upphovsrättsinnehavaren av detta verk, publicerar härmed det under följande licenser:
Denna fil har gjorts tillgänglig under licensen Creative Commons Erkännande-Dela Lika 3.0 Generisk
Erkännande: Dino på engelska Wikipedia
- Du är fri:
- att dela – att kopiera, distribuera och sända verket
- att remixa – att skapa bearbetningar
- På följande villkor:
- erkännande – Du måste ge lämpligt erkännande, ange en länk till licensen och indikera om ändringar har gjorts. Du får göra det på ett lämpligt sätt, men inte på ett sätt som antyder att licensgivaren stödjer dig eller din användning.
- dela lika – Om du remixar, transformerar eller bygger vidare på materialet måste du distribuera dina bidrag under samma eller en kompatibel licens som originalet.
|
Tillstånd ges att kopiera, distribuera och/eller modifiera detta dokument under villkoren i GNU Free Documentation License, Version 1.2 eller senare version publicerad av Free Software Foundation, utan oföränderliga avsnitt, framsidestexter eller baksidestexter. En kopia av licensen ingår i avsnittet GNU Free Documentation License. |
Du får själv välja den licens du vill använda.
Ursprunglig uppladdningslogg
Den ursprungliga beskrivningssidan fanns här. Alla följande användarnamn finns på en.wikipedia.
- 2008-03-23 18:33 Dino 1200×1200×7 (344780 bytes) {{Information |Description=Animated construction of Sierpinski Triangle |Source=self-made |Date=March 23, 2008 |Location=Boulder, Colorado |Author=~~~ |other_versions= }} Self-made. Will post source code later.
Filhistorik
Klicka på ett datum/klockslag för att se filen som den såg ut då.
| Datum/Tid | Miniatyrbild | Dimensioner | Användare | Kommentar | |
|---|---|---|---|---|---|
| nuvarande | 10 februari 2011 kl. 02.41 | | 950 × 980 (375 kbyte) | wikimediacommons>Deanmoore | Seemingly better version |
Filanvändning
Följande 2 sidor använder den här filen:
