LOGO-L> many one-liners

[JENEVOLD@aol.com]

Paolo Passaro sent me the following:

<<

I am a teacher and I use Logo in my schoolroom with my students.
but these are only my tests. Student of 6-8 grades does not do
trigonometry.   

; five_rose
repeat 1800 [rt repcount fd 10 lt repcount fd 5 rt repcount rt .1]
; ten_rose
repeat 3600 [rt repcount fd 10 lt repcount fd 1 rt repcount rt .2]

; The first 14-word command draws five roses around a five arcs,
; the second one draws ten roses around ten arcs.
; There is a repeat of 1800 times against a final right 0.1, while in 
; the second there is a repeat of 3600 times against a right 0.2, now
; I ask what is the relation between 1800,0.1 and 3600,0.2.
; What numbers I get (->1800/0.1) for drawing a six or a eight roses
; picture?

; Here is some variations of spirals:
; Eye:
repeat 1800 [fd ln repcount bk 10*sin repcount rt 10]
; growing
repeat 360 [repeat repcount [repeat repcount [fd repcount lt 15] home] lt 1]
; DonChisciotte (Don Quixote)
px repeat 360 [repeat repcount [repeat repcount [fd repcount lt 15] home] lt
1]

; And this is a 14-word command to draw circles and ellipses:
repeat 360 [rt repcount fd 1 lt repcount*2 fd 0.5 rt repcount]
; The value e=0.5 is responsible for it all (see Abelson-Di Sessa:
; "Turtle geometry", about how it works)
; it is the 'eccentricity' of the curve: if e=0 you have a circle and
; if e<0 or e>0 you have an ellipse (horizontal or vertical).

;Finally these are variations on polygons:
repeat 4 [repeat 30 [lt 90 fd 4 rt 90 fd 4] rt 90]
repeat 4 [repeat 20 [lt 160 fd 20 rt 160 fd 20] rt 90]
repeat 8 [repeat 20 [lt 170 fd 20 rt 170 fd 20] rt 45]

About legal/illegal instruction in one-line challenge I think that
the suggested mode grants the instruction "for [...]" while it is not
a primitive in most Logo dialects. Even 'repcount' is not available,
but I have used it.

Somebody can tell me how to reduce this procedure to a 15-word command?
define "tt [[l n][ifelse :n<1 [fd :l rt 120 stop]
[repeat 3 [fd :l/2 rt 120 tt :l/2 :n-1 fd :l/2 rt 120]]]
tt 300 6

My english might be wrong, please correct it for me.
Thank you.
Paolo Passaro
Biella, Italy
paspal@bienet.it

>>

These are great one-liners.

I replied to the last question as follows:

I'm sorry I cannot reduce the last fractal to 15 words.
We have been trying to make a real fractal in 15 words,
but we have not succeeded yet.
We can make a triangle fractal similar to yours
in 19 words (based on a fractal from M.H. Elhefni):

define "s [[l][if :l > 5 [repeat 3 [fd :l s :l/2 rt 120]]] s 100

- Keith Enevoldsen


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