Difference between revisions of "Sierpinski Assignment"

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(Created page with "=Sierpiński Triangle= [https://en.wikipedia.org/wiki/Sierpi%C5%84ski_triangle Sierpiński Triangle] none|frame|n=0 File:Sierpinski-trian...")
 
 
(35 intermediate revisions by the same user not shown)
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=Sierpiński Triangle=
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=Motivation=
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We will recursively generate some images with the [https://docs.racket-lang.org/teachpack/2htdpimage.html Racket Image Library].
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=Code To Investigate=
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===placement===
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._beside%29%29 beside]
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._above%29%29 above]
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* [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]
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._rotate%29%29 rotate]
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===shapes===
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._triangle%29%29 triangle]
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._circle%29%29 circle]
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._square%29%29 square]
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._rectangle%29%29 rectangle]
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* [https://docs.racket-lang.org/teachpack/2htdpimage.html#%28def._%28%28lib._2htdp%2Fimage..rkt%29._frame%29%29 frame]
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==Spacer==
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<nowiki>; fully transparent rectangle
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(define (spacer-rect w h)
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  (rectangle w h "outline" (color 0 0 0 0)))
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; fully transparent image the size of img
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(define (spacer-image img)
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  (spacer-rect (image-width img) (image-height img)))</nowiki>
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=Code To Implement=
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{{RacketToImplement|sierpinski|sierpinski-triangle<br>sierpinski-carpet|sierpinski}}
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==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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[[File:Sierpinski-triangle_0.svg|none|frame|n=0]]
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<nowiki>(define (sierpinski-triangle side-length n)
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[[File:Sierpinski-triangle_1.svg|none|frame|n=1]]
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  (raise 'not-yet-implemented #t))</nowiki>
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[[File:Sierpinski-triangle_2.svg|none|frame|n=2]]
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[[File:Sierpinski-triangle_3.svg|none|frame|n=3]]
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{| class="wikitable" style="text-align: center; "
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[[File:Sierpinski-triangle_4.svg|none|frame|n=4]]
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|[[File:Sierpinski-triangle_0.svg|200px]]
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|[[File:Sierpinski-triangle_1.svg|200px]]
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|[[File:Sierpinski-triangle_2.svg|200px]]
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|[[File:Sierpinski-triangle_3.svg|200px]]
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|[[File:Sierpinski-triangle_4.svg|200px]]
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|-
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|n=0
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|n=1
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|n=2
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|n=3
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|n=4
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|}
  
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[[File:Sierpinski-carpet_0.svg|none|frame|n=0]]
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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.
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[[File:Sierpinski-carpet_1.svg|none|frame|n=1]]
 
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[[File:Sierpinski-carpet_2.svg|none|frame|n=2]]
 
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[[File:Sierpinski-carpet_3.svg|none|frame|n=3]]
 
  
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=Cantor=
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==Carpet==
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[https://en.wikipedia.org/wiki/Cantor_set Cantor set]
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<nowiki>(define (sierpinski-carpet side-length n)
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[[File:Cantor-stool_0.svg|none|frame|n=0]]
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  (raise 'not-yet-implemented #t))</nowiki>
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[[File:Cantor-stool_1.svg|none|frame|n=1]]
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{| class="wikitable" style="text-align: center; "
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[[File:Cantor-stool_2.svg|none|frame|n=2]]
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|[[File:Sierpinski-carpet_0.svg|200px]]
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[[File:Cantor-stool_3.svg|none|frame|n=3]]
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|[[File:Sierpinski-carpet_1.svg|200px]]
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[[File:Cantor-stool_4.svg|none|frame|n=4]]
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|[[File:Sierpinski-carpet_2.svg|200px]]
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|[[File:Sierpinski-carpet_3.svg|200px]]
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|[[File:Sierpinski-carpet_4.svg.png|200px]]
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|-
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|n=0
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|n=1
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|n=2
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|n=3
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|n=4
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|}

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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