lambdaway :: stars

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_h1 ... [[koch]] | stars

_p Exploring some figures generated by turtle's moves, I discovered these strange ones.

_p 1) We define a unique sequence of turtle's moves generating five segments

{center 
 {code M'{* 2 :d} T-:a  M:d  T-:a M'{* 2 :d} T:a M'{* 3 :d} T:a M:d T:a}
}

{pre
'{def star
 {lambda {:n :d :a}            // :d is size and :a is angle
  {if {< :n 1} then else
     M{* 2 :d} T-:a 
     M:d       T-:a 
     M{* 2 :d} T:a 
     M{* 3 :d} T:a 
     M:d       T:a
     {star {- :n 1} :d :a}
}}}
-> {def star
 {lambda {:n :d :a}
   {if {< :n 1} then else
     M{* 2 :d} T-:a 
     M:d       T-:a 
     M{* 2 :d} T:a 
     M{* 3 :d} T:a 
     M:d       T:a
     {star {- :n 1} :d :a}
}}}
}

_p 2) We call it iteratively to draw a range of closed waving shapes with different values for the angle and the number of iterations:

{pre
'{def stars
 {lambda {:i}
  {polyline 
   {@ points="{turtle 370 450 {* :i 10} {star :i 10 {/ 360 :i}}}"
      fill="{if {= :i 3} then cyan else 
            {if {= :i 4} then red else #ffa}}"  
      stroke="black" 
      stroke-width="1"}}}}
-> {def stars
 {lambda {:i}
  {polyline 
   {@ points="{turtle 370 450 {* :i 10}
              {star :i 10 {/ 360 :i}}}"
      fill="{if {= :i 3} then cyan else 
            {if {= :i 4} then red else #ffa}}"  
      stroke="black" 
      stroke-width="1"}}}}

'{svg 
 {@ width="600px" height="600px" 
    style="border:1px solid #888; background:#fff;"}
 {S.map stars {S.serie 16 3 -1}}
}

}
{svg 
 {@ width="600px" height="600px" 
    style="border:1px solid #888; background:#444;"}
 {S.map stars {S.serie 16 3 -1}}
}

_p 3) The result is quite strange, looking like a kind of brain growing from two first shapes, in cyan (3x120°) and red (4x90°), rather inexpected, so different and symbolically very impressive.

{svg 
 {@ width="600px" height="230px" 
    style="border:1px solid #888; background:#fff;"}

{polyline 
  {@ points="{turtle 200 60 30 {star 3 60 {/ 360 3}}}"
     fill="transparent" stroke="grey" stroke-width="1"}}

{polyline 
  {@ points="{turtle 200 60 30 {star 1 60 {/ 360 3}}}"
     fill="transparent" stroke="cyan" stroke-width="3"}}

{polyline 
  {@ points="{turtle 480 15 0 {star 4 40 {/ 360 4}}}"
     fill="transparent" stroke="grey" stroke-width="1"}}

{polyline 
  {@ points="{turtle 480 15 0 {star 1 40 {/ 360 4}}}"
     fill="transparent" stroke="red" stroke-width="3"}}
}

_p The [[Star of David|https://en.wikipedia.org/wiki/Star_of_David]] and the [[Sauwastika|https://en.wikipedia.org/wiki/Sauwastika]] (the backwards svastika) look to be in the brain's heart? What does it mean exactly?

_p And what about the next one (5x72°)? Would it be the star of the {b XXI{sup fst}} century?

{svg 
 {@ width="600px" height="330px" 
    style="border:1px solid #888; background:#fff;"}

{polyline 
  {@ points="{turtle 300 20 0 {star 5 30 {/ 360 5}}}"
     fill="transparent" stroke="grey" stroke-width="1"}}

{polyline 
  {@ points="{turtle 300 20 0 {star 1 30 {/ 360 5}}}"
     fill="transparent" stroke="red" stroke-width="3"}}
}

{img {@ src="http://lambdaway.free.fr/workshop/data/digital_brain.jpg" width="100%" title="Digital brain"}}

{style ;;
#page_frame { width:620px; }
}