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Offline SierraKen

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Fractal Fern
« on: August 06, 2020, 12:53:27 am »
This might have been posted before. But I just found out how to make a fractal fern leaf. I'll post the URL below as well as the original code and also my own mod of it swaying in the wind. :)
Thanks to a friend of mine who found this code for me.

The code is from here: https://en.wikipedia.org/wiki/Barnsley_fern

Original (I added the URL):

Code: QB64: [Select]
  1. 'From: https://en.wikipedia.org/wiki/Barnsley_fern
  3. WINDOW (-5, 0)-(5, 10)
  8.         CASE IS < .01
  9.             nextX = 0
  10.             nextY = .16 * y
  11.         CASE .01 TO .08
  12.             nextX = .2 * x - .26 * y
  13.             nextY = .23 * x + .22 * y + 1.6
  14.         CASE .08 TO .15
  15.             nextX = -.15 * x + .28 * y
  16.             nextY = .26 * x + .24 * y + .44
  17.         CASE ELSE
  18.             nextX = .85 * x + .04 * y
  19.             nextY = -.04 * x + .85 * y + 1.6
  20.     END SELECT
  21.     x = nextX
  22.     y = nextY
  23.     PSET (x, y)
  25.  


Here is my own mod version of it swaying in the wind:

Code: QB64: [Select]
  1. 'Original Fern From: https://en.wikipedia.org/wiki/Barnsley_fern
  3. WINDOW (-5, 0)-(5, 10)
  6. x2 = 1
  8.     _LIMIT 10
  9.     FOR t = 1 TO 100000
  10.         SELECT CASE RND
  11.             CASE IS < .01
  12.                 nextX = 0
  13.                 nextY = .16 * y
  14.             CASE .01 TO .08
  15.                 nextX = .2 * x - .26 * y
  16.                 nextY = .23 * x + .22 * y + 1.6
  17.             CASE .08 TO .15
  18.                 nextX = -.15 * x + .28 * y
  19.                 nextY = .26 * x + .24 * y + .44
  20.             CASE ELSE
  21.                 nextX = .85 * x + .04 * y
  22.                 nextY = -.04 * x + .85 * y + 1.6
  23.         END SELECT
  24.         x = nextX
  25.         y = nextY
  26.         x = x + xx
  27.         PSET (x, y)
  28.     NEXT t
  29.     _DISPLAY
  30.     CLS
  31.     IF xx > .75 THEN x2 = 2
  32.     IF xx < -.75 THEN x2 = 1
  33.     IF x2 = 1 THEN xx = xx + .1
  34.     IF x2 = 2 THEN xx = xx - .1
  36.  
« Last Edit: August 06, 2020, 12:56:37 am by SierraKen »
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Offline SierraKen

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Re: Fractal Fern
« Reply #1 on: August 06, 2020, 01:00:43 am »
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Offline johnno56

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Re: Fractal Fern
« Reply #2 on: August 06, 2020, 01:42:19 am »
The Fern I had seen before but the "swaying" version was a nice twist... Nice job as both draw very quickly....

Ah... The classic Mandelbrot... That was pretty quick too... Oh, you just have to love QB's palette of colours...

Can't go past Fractals and Brots.... Cool... ;)
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Offline bplus

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Re: Fractal Fern
« Reply #3 on: August 06, 2020, 12:33:06 pm »
Yes nice twist:
Code: QB64: [Select]
  1. _TITLE "Classic Fern sway in wind mod, press spacebar for new landscape, esc to quit" 'b+ 2020-08-06
  2. SCREEN _NEWIMAGE(1000, 600, 32)
  3. _DELAY .25
  5. WINDOW (-5, 0)-(5, 11)
  7.  
  8. TYPE obj
  9.     x AS SINGLE 'offset from centered fern
  10.     y AS SINGLE 'offest from centered fern
  11.     scale AS SINGLE ' from 0 to 1
  12.     c AS _UNSIGNED LONG
  14.  
  15. DIM SHARED nFerns
  16. REDIM SHARED fern(1 TO nFerns) AS obj
  17.  
  18. initFerns
  19. wind = 0: dw = .01: dir = 1
  20. WHILE _KEYDOWN(27) = 0
  21.     IF INKEY$ = " " THEN initFerns
  22.     FOR i = 4 TO 11 STEP .2
  23.         LINE (-5, i)-(5, i + .2), _RGB32(60, (1 - i / 11) * 150 + 60, (1 - i / 11) * 75 + 180), BF
  24.     NEXT
  25.     FOR i = 0 TO 4 STEP .2
  26.         LINE (-5, i)-(5, i + .2), _RGB32(i / 4 * 90 + 10, i / 4 * 45 + 5, i / 4 * 22 + 2), BF
  27.     NEXT
  28.     FOR i = 1 TO nFerns
  29.         drawFern fern(i).x, fern(i).y, fern(i).scale, fern(i).c, wind
  30.     NEXT
  31.  
  32.     _DISPLAY
  33.     _LIMIT 10
  34.     wind = wind + dir * dw
  35.     IF wind > .06 OR wind < -.72 THEN dir = -dir
  37.  
  38. SUB initFerns
  39.     nFerns = 4 + INT(RND * 9)
  40.     REDIM fern(1 TO nFerns) AS obj
  41.     FOR i = 1 TO nFerns
  42.         fern(i).x = RND * 10 - 5
  43.         fern(i).y = RND * 2 - 1
  44.         fern(i).scale = RND * .7 + .3
  45.         g = RND * 100 + 40
  46.         fern(i).c = _RGB32(g - 20 - RND * 60, g, g - 20 - RND * 60)
  47.     NEXT
  49.  
  50. SUB drawFern (xoff0, yoff0, scale, c AS _UNSIGNED LONG, w)
  51.     yAdj = yoff0 + (1 - scale) * 5
  52.     FOR i = 1 TO 90000 'enough dots to get idea
  53.         SELECT CASE RND
  54.             CASE IS < .01
  55.                 nextX = 0
  56.                 nextY = .16 * y
  57.             CASE .01 TO .08
  58.                 nextX = .2 * x - .26 * y
  59.                 nextY = .23 * x + .22 * y + 1.6
  60.             CASE .08 TO .15
  61.                 nextX = -.15 * x + .28 * y
  62.                 nextY = .26 * x + .24 * y + .44
  63.             CASE ELSE
  64.                 nextX = .85 * x + .04 * y
  65.                 nextY = -.04 * x + .85 * y + 1.6
  66.         END SELECT
  67.         x = nextX + w * nextY / 10
  68.         y = nextY
  69.         LINE (x * scale + xoff0, y * scale + yAdj)-STEP(0, 0), c, BF
  70.     NEXT
  72.  
  73.  

It's amazing how much hand drawn graphics can be executed in a second!
« Last Edit: August 06, 2020, 12:51:22 pm by bplus »
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Offline SierraKen

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Re: Fractal Fern
« Reply #4 on: August 06, 2020, 04:38:15 pm »
Awesome mod Bplus, more realistic swaying than mine is, I'll have to check out the code.

Yep Johno, the stuff you can find buried online... there's amazing gems out there.
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Offline bplus

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Re: Fractal Fern
« Reply #5 on: August 06, 2020, 08:13:23 pm »
Dang! It's back again!

 
It's back again!.PNG
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Offline johnno56

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Re: Fractal Fern
« Reply #6 on: August 06, 2020, 08:58:58 pm »
Amazing! The things you find hiding in the grass....
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Offline SierraKen

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Re: Fractal Fern
« Reply #7 on: August 06, 2020, 09:43:22 pm »
ROFL! I bet that looks amazing with the animation.
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Offline Ashish

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Re: Fractal Fern
« Reply #8 on: August 06, 2020, 11:57:44 pm »
Good job, @bplus and @SierraKen :-)
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Offline SierraKen

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Re: Fractal Fern
« Reply #9 on: August 07, 2020, 12:04:45 am »
Thanks Ashish, it wasn't too hard for me since I just added a few lines to the code I found online.
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Offline Ashish

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Re: Fractal Fern
« Reply #10 on: August 07, 2020, 12:10:14 am »
Sierra, if you are interesed, you can see a collection of fractals in QB64 here - https://www.qb64.org/forum/index.php?topic=182
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Offline SierraKen

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Re: Fractal Fern
« Reply #11 on: August 07, 2020, 01:56:02 am »
Ashish, I am awe-struck. I have no idea how you did those. Is there a trick to it? How did you get all the numbers? I don't know one thing about making these. I saved all of yours to my hard drive. There was one though called Leaf (number 6) that wouldn't work. It tries to work but the window quickly vanishes and doesn't show anything. You might want to take a look at it. But I am just amazed how good that is. Especially the plants and trees. I guess I never got that advanced in math or something. lol
« Last Edit: August 07, 2020, 01:57:06 am by SierraKen »
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Offline bplus

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Re: Fractal Fern
« Reply #12 on: August 07, 2020, 12:51:47 pm »
Thanks @Ashish

Ken's right that Leaf fractal #6 won't even put up a screen, I tried a couple things but still not working.

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Offline Ashish

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Re: Fractal Fern
« Reply #13 on: August 07, 2020, 01:03:26 pm »
@SierraKen
The equations were originally taken from here - http://paulbourke.net/fractals/ifs/

About Leaf fractal : It does works on my machine.
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Offline _vince

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Re: Fractal Fern
« Reply #14 on: August 07, 2020, 09:21:18 pm »
Quote from: SierraKen on August 06, 2020, 01:00:43 am
Check this fractal out as well, a Mandelbrot:

https://github.com/adamlwgriffiths/qbasic-fractal/blob/master/MANDELBR.BAS

Must be a good time for me to plug mine:
Code: QB64: [Select]
  1. defint a-z
  2.  
  3. const sw = 640
  4. const sh = 480
  5.  
  6. dim shared mx,my,mbl,mbr,mw
  7.  
  13. z = 0.01
  14. zz = 0.1
  15.  
  17. p1 = _newimage(sw, sh, 32)
  18. screen _newimage(sw, sh, 32)
  19.  
  20. redraw = -1
  21. iter = 100
  22.  
  23. dim c(100) as long, cc as long
  24.  
  25. for i=0 to iter-1
  26.         if i < iter/6 then
  27.                 r = 155
  28.                 g = (i mod (iter/6))*(255/(iter/6))
  29.                 b = 0
  30.         elseif i < 2*iter/6 then
  31.                 r = 155 - (i mod (iter/6))*(255/(iter/6))
  32.                 g = 155
  33.                 b = 0
  34.         elseif i < 3*iter/6 then
  35.                 r = 0
  36.                 g = 155
  37.                 b = (i mod (iter/6))*(255/(iter/6))
  38.         elseif i < 4*iter/6 then
  39.                 r = 0
  40.                 g = 155 - (i mod (iter/6))*(255/(iter/6))
  41.                 b = 155
  42.         elseif i < 5*iter/6 then
  43.                 r = (i mod (iter/6))*(255/(iter/6))
  44.                 g = 0
  45.                 b = 155
  46.         else
  47.                 r = 155
  48.                 g = 0
  49.                 b = 155 - (i mod (iter/6))*(255/(iter/6))
  50.         end if
  51.         c(i) = _rgb(r, g, b)
  53.  
  55.         mw = 0
  56.         getmouse
  57.  
  58.         if redraw then
  59.                 for y = 0 to sh-1
  60.                 for x = 0 to sw-1
  61.                         u = 0
  62.                         v = 0
  63.  
  64.                         xx = (x - sw/2)*z + x0
  65.                         yy = (y - sh/2)*z + y0
  66.                         for i = 0 to iter
  67.                                 '''mandelbrot
  68.                                 uu = u*u - v*v + xx
  69.                                 vv = 2*u*v + yy
  70.                                 '''
  71.  
  72.                                 '''burning ship
  73.                                 'u = abs(u)
  74.                                 'v = abs(v)
  75.                                 'uu = u*u - v*v + xx
  76.                                 'vv = 2*u*v + yy
  77.                                 '''
  78.  
  79.                                 '''tricorn
  80.                                 'u = u
  81.                                 'v = -v
  82.                                 'uu = u*u - v*v + xx
  83.                                 'vv = 2*u*v + yy
  84.                                 '''
  85.  
  86.                                 '''tetration
  87.                                 'u = u
  88.                                 'v = v
  89.                                 'cexp uu, vv, u, v, u, v
  90.                                 'cexp uu, vv, uu, vv, xx, yy
  91.                                 '''
  92.  
  93.                                 u = uu
  94.                                 v = vv
  95.  
  96.                                 if (u*u + v*v) > 4 then exit for
  97.                         next
  98.                         if i > iter then
  99.                                 pset(x, y), _rgb(0,0,0)
  100.                         else
  101.                                 pset(x, y), c(i mod 100)
  102.                         end if
  103.                 next
  104.                 next
  105.  
  106.                 'locate 1,1
  107.                 'print "iter =";iter
  108.                 _title str$(iter)
  109.  
  110.                 _dest p1
  111.                 _putimage , 0
  112.                 _dest 0
  113.  
  114.                 _putimage , p1
  115.                 _autodisplay
  116.  
  117.                 redraw = 0
  118.         end if
  119.  
  120.         if mw < 0 then
  121.                 zz = zz + 0.01
  122.         elseif mw > 0 then
  123.                 if zz > 0.01 then zz = zz - 0.01
  124.         end if
  125.  
  126.         'draw box
  127.         if omx <> mx or omy <> my or mw <> 0 then
  128.                 _putimage , p1
  129.                 line (mx - (sw*zz/2), my - (sh*zz/2))-step(sw*zz,sh*zz),_rgb(255,255,255),b
  130.                 _autodisplay
  131.  
  132.                 omx = mx
  133.                 omy = my
  134.         end if
  135.  
  136.         if mbl then
  137.                 do
  138.                         getmouse
  139.                 loop while mbl
  140.  
  141.                 x0 = x0 + (mx - sw/2)*z
  142.                 y0 = y0 - (sh/2 - my)*z
  143.                 z = z*zz
  144.  
  145.                 iter = iter + 50
  146.  
  147.                 redraw = -1
  148.         elseif mbr then
  149.                 do
  150.                         getMouse
  151.                 loop while mbr
  152.  
  153.                 x0 = x0 + (mx - sw/2)*z
  154.                 y0 = y0 - (sh/2 - my)*z
  155.                 z = z/zz
  156.                 redraw = -1
  157.         end if
  158.  
  159.         k = _keyhit
  160.         if k = 43 then
  161.                 iter = iter + 50
  162.                 redraw = -1
  163.         elseif k = 45 then
  164.                 if iter > 50 then iter = iter - 50
  165.                 redraw = -1
  166.         end if
  167.  
  168. loop until k = 27
  170.  
  171. sub getmouse ()
  172.         do
  173.                 mx = _mousex
  174.                 my = _mousey
  175.                 mbl = _mousebutton(1)
  176.                 mbr = _mousebutton(2)
  177.                 mw = mw + _mousewheel
  178.         loop while _mouseinput
  180.  
  181. 'u + iv = (x + iy) ^ (a + ib)
  182. sub cexp (u as double, v as double, x as double, y as double, a as double, b as double)
  183.         dim mag as double, arg as double
  184.         dim lnz as double, argz as double
  185.  
  186.         lnz = 0.5*log((x*x + y*y)+0.00001)
  187.         argz = _atan2(y, x)
  188.  
  189.         mag = exp(a*lnz - b*argz)
  190.         arg = a*argz + b*lnz
  191.  
  192.         u = mag * cos(arg)
  193.         v = mag * sin(arg)
  195.  
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