LOGO-L> Re: Chaotic Gasket

[Mordechai Shorek <kuny@mofet.macam98.ac.il>]

YUDA

RETHANKS as usual

is the 1/3 at stage 2 obligatory ?
try 1/4 !!!

m


Yehuda Katz wrote:

> Hello there,
>
> The Sierpinski Triangle was discussed, sometime ago, on this list.
> Here's a "square" version of it.
> There are several ways to do it, this one  does it chaotically by
> Logo's RND function.
>
> The algorithm is as follows:
>
> Find the locations of the four corners of a square and the locations
> of the centers of its sides. These are 8 points.
> Place yourself anywhere on the screen.
>
> 1.      Select at random one of the 8 points.
> 2.      From your position move one third of the distance towards that
> selected point.
> 3.      Mark this point, and position yourself on it.
> 4.      Return to 1.
>
> Here's a possible Logo program to perform the above algorithm:
>
> ======================================
> to main                       ; Gasket
> cs ht
> select rndpt 0
> end
>
> to select :pnt :dummy
> setpc last :pnt
> pu setxy x y pd
> if :dummy>5[fd 0]         ; draw a dot
> select rndpt 1+:dummy
> end
>
> to rndpt
> op pick[
>  [-243  243 4][0  243 6][243  243 4]
>  [-243    0 6]          [243    0 6]
>  [-243 -243 4][0 -243 6][243 -243 4]]
> end
>
> to x
> op(xcor + item 1 :pnt)/3
> end
>
> to y
> op(ycor + item 2 :pnt)/3
> end
> ======================================
>
> A few remarks here might be in place:
>
> The gasket is drawn around the center of the screen.
> If you look closely at the attached drawing you might see how precise
> it is, down to the last pixel. It's because the chosen length of the
> half side of the square - 243 -  is a power of 3 (3^5).
> If the drawing is too big to fit on your screen, replace each 243 with
> 81 (=3^4).
>
> The RNDPT procedure was arranged and spaced so that the sub-list
> containing the coordinates of each of the 8 point can be recognized
> easily. You will see it better in a non-proportional font, like
> COURIER.
> The last member in each sub-list is the dot color.
>
> The first few points fluctuate a little bit until settling down, so I
> made the program ignore the first 5 (DUMMY) points.
>
> I didn't include in my program a stop rule, you must stop it by brute
> force.
>
> Let the program run for a few minutes, and see how, like a miracle,
> the "gasket" builds up.
>
> The program was written in UCBLogo, but will run, I think, on any
> other flavor of Logo.
>
> Enjoy...
>
> [[Yehuda]]
>
>
>
>
> -------------------------------------------------------------------------------------------------------------
>
>  [Image]



---------------------------------------------------------------
Please post messages to the Logo forum to logo-l@gsn.org.  Mail
questions about the list administration to logofdn@gsn.org.  To
unsubscribe send    unsubscribe logo-l    to majordomo@gsn.org.