lambdaway :: goldenrect

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_img ../lambdaspeech/data/Animation_Fibonacci.gif

_h1 golden rect

{pre
'{def fibonacci
 {lambda {:n} 
  {if {< :n 2}
   then 1
   else {+ {fibonacci {- :n 1}} {fibonacci {- :n 2}}}}}}
-> {def fibonacci
 {lambda {:n} 
  {if {< :n 2}
   then 1
   else {+ {fibonacci {- :n 1}} {fibonacci {- :n 2}}}}}}

'{def F {A.new {S.map fibonacci {S.serie 0 10}}}}
-> {def F {A.new {S.map fibonacci {S.serie 0 10}}}} = {F}¥

'{def goldrect    
 {lambda {:x :y :a}
  {turtle :x :y 0
   {S.map {{lambda {:a :i} {square :a {A.get :i {F}}}
           } :a} 
          {S.serie 10 0 -1}}}}}
-> {def goldrect    
 {lambda {:x :y :a}
  {turtle :x :y 0 {S.map {{lambda {:a :i} {square :a {A.get :i {F}}}} :a} {S.serie 10 0 -1}}}}}

'{def square
 {lambda {:a :d} 
      M:d T90 M:d T90 M:d T90 M:d T90 M:d T90 M:d T:a}}
-> {def square {lambda {:a :d} M:d T90 M:d T90 M:d T90 M:d T90 M:d T90 M:d T:a}}

'{def stroke
 {lambda {:c} 
  stroke=":c" stroke-width="1" fill="transparent"}}
-> {def stroke {lambda {:c} stroke=":c" stroke-width="1" fill="transparent"}}
}

_h2 display 1

{pre
'{center
 {svg {@ width="500" height="500" style="background:#444"}
      {g {@ transform="scale(2.5,2.5)" } 
         {path {@ d="M {goldrect 10 50 -15}" {stroke #888}}}
}}}

}

{center
 {svg {@ width="500" height="500" style="background:#444"}
  {g {@ transform="scale(2.5,2.5)" } 
 {path {@ d="M {goldrect 10 50 -15}" {stroke #888}}}
}}}

_h2 display 2

{pre
'{center
 {svg {@ width="500" height="500" style="background:#444"}

{path {@ d="M {goldrect 200 10 -15}" {stroke #888}}}
 {path {@ d="M {goldrect 200 10 0}" {stroke #fff}}}

{path {@ d="M {goldrect 200 110 -30}" {stroke #888}}}
 {path {@ d="M {goldrect 200 110 -60}" {stroke #888}}}
 {path {@ d="M {goldrect 200 110 -45}" {stroke #fff}}}

{path {@ d="M {goldrect 200 210 -75}" {stroke #888}}}
 {path {@ d="M {goldrect 200 210 -105}" {stroke #888}}}
 {path {@ d="M {goldrect 200 210 -90}" {stroke #fff}}}

{path {@ d="M {goldrect 100 210 -120}" {stroke #888}}}
 {path {@ d="M {goldrect 100 210 -150}" {stroke #888}}}
 {path {@ d="M {goldrect 100 210 -135}" {stroke #fff}}}

{path {@ d="M {goldrect 100 10 -165}" {stroke #888}}}
 {path {@ d="M {goldrect 100 10 -180}" {stroke #fff}}}
}}
}

{center {svg {@ width="500" height="500" style="background:#444"}

{path {@ d="M {goldrect 200 10 -15}" {stroke #888}}}
 {path {@ d="M {goldrect 200 10 0}" {stroke #fff}}}

{path {@ d="M {goldrect 200 110 -30}" {stroke #888}}}
 {path {@ d="M {goldrect 200 110 -60}" {stroke #888}}}
 {path {@ d="M {goldrect 200 110 -45}" {stroke #fff}}}

{path {@ d="M {goldrect 200 210 -75}" {stroke #888}}}
 {path {@ d="M {goldrect 200 210 -105}" {stroke #888}}}
 {path {@ d="M {goldrect 200 210 -90}" {stroke #fff}}}

{path {@ d="M {goldrect 100 210 -120}" {stroke #888}}}
 {path {@ d="M {goldrect 100 210 -150}" {stroke #888}}}
 {path {@ d="M {goldrect 100 210 -135}" {stroke #fff}}}

{path {@ d="M {goldrect 100 10 -165}" {stroke #888}}}
 {path {@ d="M {goldrect 100 10 -180}" {stroke #fff}}}
}}

_h2 display 3

{pre
'{center 
{svg {@ width="500" height="500" style="background:#fff"}
     {g {@ transform="translate(250,-50) rotate(45)" }
     {S.map {lambda {:i} {path {@ d="M {goldrect 100 100 :i}"
                                  {stroke #000}}} }
            {S.serie 0 360 10}}}}}
}

{center 
{svg {@ width="500" height="500" style="background:#fff"}
 {g {@ transform="translate(250,-50) rotate(45)" }
 {S.map {lambda {:i}
                {path {@ d="M {goldrect 100 100 :i}" {stroke #000}}} }
        {S.serie 0 360 10}}}
}}
{center Big Brother is watching you}

_p To be compared with a similar code found in page 132 of " Racket Programming the Fun Way", James W. Stelly

{pre
 ; function to compute F(n)

(define (F n)
    (define (f a b cnt)
      (if (= cnt 0) b
          (f (+ a b) a (- cnt 1))))
    (f 1 0 n))
  
 ; function to draw the tiling

(define (draw-n n)
   (let* ([fn (F n)]
         [sn (* UNIT fn)]
         [fn1 (F (sub1 n))]
         [sn1 (* UNIT fn1)]
          [n-mod-4 (remainder n 4)])
     (cond [(< n 2) #f] ; do nothing tiles already drawn
           [(= n 2) (values (+ UNIT START-X) START-Y START-X START-Y)]
           [else
           (let-values ([(x1 y1 x2 y2) (draw-n (sub1 n))])
              (let-values ([(x y)
                            (case n-mod-4
                             [(0) (values (- x1 sn) y1)]
                             [(1) (values x1 (+ y1 sn1))]
                             [(2) (values (+ x1 sn1) y2)]
                             [(3) (values x2 (- y1 sn))])])
                (draw-tile x y sn)
                (values x y x1 y1)))])))

(define (draw-tiles n)
  (draw-tile START-X START-Y UNIT)
  (draw-tile (+ UNIT START-X) START-Y UNIT)
  (draw-n n)
  (print tiling))

Listing 4-1: Fibonacci with Tiling »
}

_h2 see also

_img http://b2b3.free.fr/confs/data/modulor_3/palacio_fibonacci.jpg
_img http://marty.alain.free.fr/architecture/immeuble/palazzio.JPG
_img https://s2.qwant.com/thumbr/700x0/4/7/1a3e815ff8720539809241e45bbb973ab285be095dab1f216b8a6f725eeda8/1200px-Punched_card.jpg?u=https%3A%2F%2Fupload.wikimedia.org%2Fwikipedia%2Fcommons%2Fthumb%2Ff%2Ff3%2FPunched_card.jpg%2F1200px-Punched_card.jpg&q=0&b=1&p=0&a=1
_img https://s2.qwant.com/thumbr/0x380/5/4/ba73a881eec5a5456e154b86d52790d12b9dfe159aa0cdab3a36554a05327d/sd-me-zoo-elephant-20170315.jpg?u=https%3A%2F%2Fwww.trbimg.com%2Fimg-58c9ed44%2Fturbine%2Fsd-me-zoo-elephant-20170315&q=0&b=1&p=0&a=1