Difference between revisions of "Sierpinski Assignment"

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=Code To Investigate=
 
=Code To Investigate=
 
===placement===
 
===placement===
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._beside%29%29 beside]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._beside%29%29 beside]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._above%29%29 above]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._above%29%29 above]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._overlay%29%29 overlay] [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._overlay%2Falign%29%29 overlay/align]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._overlay%29%29 overlay] [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._overlay%2Falign%29%29 overlay/align]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._rotate%29%29 rotate]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._rotate%29%29 rotate]
 
===shapes===
 
===shapes===
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._triangle%29%29 triangle]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._triangle%29%29 triangle]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._circle%29%29 circle]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._circle%29%29 circle]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._square%29%29 square]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._square%29%29 square]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._rectangle%29%29 rectangle]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._rectangle%29%29 rectangle]
−
: [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._frame%29%29 frame]
+
* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._frame%29%29 frame]
 
==Spacer==
 
==Spacer==
 
  <nowiki>; fully transparent rectangle
 
  <nowiki>; fully transparent rectangle
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   (spacer-rect (image-width img) (image-height img)))</nowiki>
 
   (spacer-rect (image-width img) (image-height img)))</nowiki>
  
−
=Sierpiński=
+
=Code To Implement=
−
{{RacketToImplement|sierpinski|sierpinski-triangle<br>sierpinski-carpet|sierpinski_and_cantor}}
+
{{RacketToImplement|sierpinski|sierpinski-triangle<br>sierpinski-carpet|sierpinski}}
 
==Triangle==
 
==Triangle==
 
[https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle Sierpiński Triangle]
 
[https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle Sierpiński Triangle]
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|}
 
|}
  
−
Note: this has a remarkably clean solution.
+
Note: this has a remarkably clean solution.  It is almost as if the [https://docs.racket-lang.org/teachpack/2htdpimage.html Racket Image Library] was created to build the Sierpiński Triangle.
  
 
==Carpet==
 
==Carpet==
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|[[File:Sierpinski-carpet_3.svg|200px]]
 
|[[File:Sierpinski-carpet_3.svg|200px]]
 
|[[File:Sierpinski-carpet_4.svg.png|200px]]
 
|[[File:Sierpinski-carpet_4.svg.png|200px]]
−
|-
 
−
|n=0
 
−
|n=1
 
−
|n=2
 
−
|n=3
 
−
|n=4
 
−
|}
 
−
 
−
=Cantor=
 
−
[https://en.wikipedia.org/wiki/Cantor_set Cantor set]
 
−
 
−
{{RacketToImplement|cantor|cantor-stool|sierpinski_and_cantor}}
 
−
 
−
==Stool==
 
−
<nowiki>(define (cantor-stool width height n)
 
−
  (raise 'not-yet-implemented #t))</nowiki>
 
−
 
−
{| class="wikitable" style="text-align: center; "
 
−
|[[File:Cantor-stool_0.svg|200px]]
 
−
|[[File:Cantor-stool_1.svg|200px]]
 
−
|[[File:Cantor-stool_2.svg|200px]]
 
−
|[[File:Cantor-stool_3.svg|200px]]
 
−
|[[File:Cantor-stool_4.svg|200px]]
 
 
|-
 
|-
 
|n=0
 
|n=0

Latest revision as of 20:36, 27 March 2023

Motivation

We will recursively generate some images with the Racket Image Library.

Code To Investigate

placement

shapes

Spacer

; fully transparent rectangle
(define (spacer-rect w h)
  (rectangle w h "outline" (color 0 0 0 0)))

; fully transparent image the size of img
(define (spacer-image img)
  (spacer-rect (image-width img) (image-height img)))

Code To Implement

file: src/main/racket/sierpinski/sierpinski.rkt Racket-logo.svg
functions: sierpinski-triangle
sierpinski-carpet

Triangle

Sierpiński Triangle 

(define (sierpinski-triangle side-length n)
  (raise 'not-yet-implemented #t))
Sierpinski-triangle 0.svg Sierpinski-triangle 1.svg Sierpinski-triangle 2.svg Sierpinski-triangle 3.svg Sierpinski-triangle 4.svg
n=0 n=1 n=2 n=3 n=4

Note: this has a remarkably clean solution. It is almost as if the Racket Image Library was created to build the Sierpiński Triangle.

Carpet

(define (sierpinski-carpet side-length n)
  (raise 'not-yet-implemented #t))
Sierpinski-carpet 0.svg Sierpinski-carpet 1.svg Sierpinski-carpet 2.svg Sierpinski-carpet 3.svg Sierpinski-carpet 4.svg.png
n=0 n=1 n=2 n=3 n=4
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