micro-contest - draw a pattern

[tsh73]

Have nothing to do?
Have a go at repeating this pattern in JB


(I was looking at student practicing graphic stuff, repeating chessboard from example.
Then I thight "It might be cool if I start with big squares, then divide them in half keeping then alternating, and continue till it get 1 pixel")

So after coming home (and finishing that other big program I just posted) I quickly draw this.
It fits to description but surprised me looking that fractalish.
It supposed to be 512x512 so it fits 1376x768 screen and divides nicely.
How small program could you get?

I will post my solution later (give folks time to show their own ideas :) )

[tenochtitlanuk]

That was fun!
I tried swapping the alternating fill on each line for aesthetic reasons, and using circles ( needed a fiddle-factor to make them touch.)

[tsh73]

I hope I did give enough time to ponder on it;)
First I did one version (surpisingly last one), then I made two others...

Approach #1.
Draw squares down - in a loop - alternating color (rather draw/not draw) - to bottom.
Then shrink square 2x, move right, repeat until size comes to 1
(happened that you can't draw BOX of single pixel size)
'rectangle version
nomainwin

N=9
desiredWidth = 2^N
desiredHeight = 2^N

gosub [ajustWindow]
'now, center window
   UpperLeftX = (DisplayWidth - WindowWidth)/2
   UpperLeftY = (DisplayHeight - WindowHeight)/2

   'now, open your window with desired size
       'with menu if you wish
   'MENU #gr, "File", "Exit", [quit]
   open "Shrinking chess pattern" for graphics_nsb_nf as #gr
'   graphics
'   graphics_nsb
'   graphics_nsb_nf

   #gr, "trapclose [quit]"
   #gr, "down"

#gr "backcolor black"

s=2^(N-1)
x=0
do
for y = 1 to 2^N-1 step s
if i mod 2 then
if s>1 then
#gr "place ";x;" ";y
#gr "boxfilled ";x+s;" ";y+s
else
#gr "set ";x;" ";y 'there no single-pixel box
end if
end if
i=i+1
next
x=x+s
s=int(s/2)
loop while s>0

   #gr "flush"

wait

'-----------------------
[quit]
   timer 0
   close #gr
   end


'-------------------------------------------------
[ajustWindow]
   UpperLeftX = 20
   UpperLeftY = 20
   WindowWidth = 200   '100 seems to be too much - works different
   WindowHeight = 100
   'MENU #gr, "dummy"
   open "Ajusting..." for graphics_nsb_nf as #gr
'   graphics
'   graphics_nsb
'   graphics_nsb_nf

   #gr, "home ; down ; posxy x y"
   'x, y give us width, height
   width = 2*x : height = 2*y
   close #gr

   slackX = 200-width
   slackY = 100-height

   WindowWidth = desiredWidth + slackX
   WindowHeight = desiredHeight + slackY

return


Part that sets window is boilerplate, I will not repeat that.

Approach #2.
Take a square; fill lower bottom quarter; call it recursively on top right, bottom right.
Recursion ends then square gets too small.
Recursive code is neat! ;)
Only inner drawing part:
#gr "backcolor black"

call draw 0, 0, 2^N
   #gr "flush"

wait

sub draw x, y, s
s=s/2
if s>1 then
#gr "place ";x;" ";y+s
#gr "boxfilled ";x+s;" ";y+2*s
call draw x+s, y, s
call draw x+s, y+s, s
else
#gr "set ";x;" ";y 'there no single-pixel box
end if
end sub


Approach #3.
After some thinking - it occured to me that each line in resulting picture corresponds to binary representation of one number from 0 to 2^N-1, where "1" is black, and line segment length is binary digit weight (that is, 2^i)
It get somewhat mangled since I imagined it with upper digit left - and it got showing backwards, so I end with 2^(10-i) and 512-x.
But I still think it's neat. Needs bin$() custom function.
   for y = 0 to 2^N
       b$=right$("000000000"+bin$(y), 9)
       for i = 1 to 9
           if mid$(b$,i,1)="1" then
               x=2^(10-i)
               #gr "line ";512-x/2;" ";y;" ";512-x;" ";y
           end if
        next
   next
   #gr "flush"

wait

'-----------------------------
function bin$(n)
   while n
       bin$=(n mod 2);bin$
       n=int(n/2)
   wend
   if bin$="" then bin$="0"
end function


[tenochtitlanuk]

I'll add a page to my site with my variations.
Interesting seeing you working around ideas --> code, Anatoly.

Meanwhile here's one for everyone- the 'Tree of Circles'.



Here's an animation of my current approach to this one!

[tenochtitlanuk]

..and now ... ( suppressing the 'inward' directions. And leaving space...




EDIT or without the spaces...



.. and my favourite ...

[tsh73]

Snowy one looks really nice, too
And nice thing about patterns - then you fail to reproduce sought pattern you might get another pretty one
(it this case I did not step from parent circle at all)

[tenochtitlanuk]

Next one I want to try is this.. wonder what I'll end with?

[tenochtitlanuk]

So I got . . .



Will be putting a page on my site soon with the code.

[tsh73]

looks like some celestial mechanic ;)
(just imagine it spin!)
I wonder if you make circles stay apart as 1/number of incoming lines?

[tsh73]

Got more on the floral side, I think :)

'along JohnFisher (tenochtitlanuk) picture
nomainwin

global pi, cx, cy, shrink
pi = acs(-1)

WindowWidth = 600
WindowHeight = 600

open "test" for graphics_nsb_nf as #gr
#gr "home; down; posxy cx cy"
#gr "trapclose [quit]"

shrink = 2
call draw cx,cy,a,0,256,0

#gr "flush"

wait

[quit]
   timer 0
   close #gr
   end

sub draw x,y,a,totLen, length, level
   SCAN
   'if level >5 then exit sub
   if length <1 then exit sub
   x1=cx+cos(a)*totLen
   y1=cy+sin(a)*totLen
   if level >0 then
       #gr "place ";x;" ";y
       #gr "goto ";x1;" ";y1
   end if

   if a = 0 and totLen>0 then
       #gr "place ";cx;" ";cy
       #gr "circle ";totLen
   end if

   N=3^(level+1)
   da=2*pi/N
   length=length/shrink
   call draw x1,y1,a-da,totLen+length,length, level+1
   call draw x1,y1,a,totLen+length,length, level+1
   call draw x1,y1,a+da,totLen+length,length, level+1
end sub

[tenochtitlanuk]

Nice one! It repays the experimentally-minded programmer. And recursion is definitely the better way..

I've re-created the original version, overlayed on the Orion constellation.

Details are on a page at Diga-Me

[tenochtitlanuk]

For amusement I threw random colours at all white areas. This needs to be run in LB for the dll. A few seconds and 10000 throws later I got