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_h1 pythagoras tree

_p After [[Allen Guo|http://aguo.us/writings/pythagoras-tree.html]], drawing a pythagoras tree using a Racket library, [[Turtle Graphics|http://docs.racket-lang.org/turtles]], 
{pre
#lang racket

; pythagoras-tree.rkt:
;   Draws a Pythagoras tree using Racket's turtle graphics library.
;   Run this program from the terminal with `racket pythagoras-tree.rkt`.

(require graphics/turtles) ; raco pkg install htdp-lib
(turtles #t)

(define (pythagoras-tree side) ; starting position: center of square, facing east
  (if (< side 3) ; this seems like a good stopping point...
      (home)     ; clear all turtles except the original
      (let ((half-side (/ side 2)))
        (turn 90)        ; now facing north
        (move half-side) ; move north
        (turn 90)        ; now facing west
        (draw half-side) ; draw west
        (turn 90)        ; now facing south
        (draw side)      ; draw south
        (turn 90)        ; now facing east
        (draw side)      ; draw east
        (turn 90)        ; now facing north
        (draw side)      ; draw north
        (turn 90)        ; now facing west
        (draw half-side) ; draw west

(turn -45)         ; turn turtle 1 (current turtle) to face northwest
        (split (turn -90)) ; create and turn turtle 2 to face northeast

(move (* half-side (sqrt 2))) ; move both turtles to the centers of the new squares
        (turn -90)                    ; and adjust them to face east
        (pythagoras-tree (* (/ (sqrt 2) 2) side))))) ; recurse!

(pythagoras-tree 100)
}

{img {@ src="data/pythagoras-tree-3.jpg" width="100%"}}

_p ... my purpose is to write my own version in lambdatalk.
{pre °°
1) logo library
{def canvas.init {lambda {} ...}
{def home {lambda {} ...}}
{def turn {lambda {:a} ...}}
{def move {lambda {:l} ...}}
{def draw {lambda {:l} ...}}
{def split {lambda {:l} ...}}

2) defining function
{def pythagoras-tree 
 {lambda {:side}
  {if {< :side 3}
   then {home}
   else {turn 90} {move {/ :side 2}}
        {turn 90} {draw {/ :side 2}}
        {turn 90} {draw :side}
        {turn 90} {draw :side}
        {turn 90} {draw :side}
        {turn 90} {draw {/ :side 2}}
        {turn -45} 
        {split {turn -90}}
        {move {* {/ :side 2} {sqrt 2}}}
        {turn -90}
        {pythagoras-tree {* {/ {sqrt 2} 2} :side}} 
}}}

3) calling function (in some canvas to define)
{{canvas.init ...}
 {pythagoras-tree 100}
}
°°}

_p Following this first attempt in page [[logo]]. Coming soon...