Author Topic: Fractal Fun  (Read 13326 times)

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Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #45 on: November 18, 2009, 10:01:40 AM »

Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #46 on: November 18, 2009, 02:09:17 PM »
Slightly off topic, and not really a fractal - but I thought you might be interested in the Butterfly Curve

This one I have made 3D

Code: [Select]
`(defun c:butterfly_curve (/ s)  (setq s (* -10.05 pi))  (entmake (list (cons 0 "POLYLINE") (cons 66 1) (cons 70 8)))  (while (<= (setq s (+ s 0.05)) (* 10. pi))    (entmake      (list (cons 0 "VERTEX") (cons 70 32)            (cons 10 (list (* (sin s) (- (exp (cos s)) (* 2. (cos (* 4. s))) (expt (sin (/ s 12.)) 5)))                           (* (cos s) (- (exp (cos s)) (* 2. (cos (* 4. s))) (expt (sin (/ s 12.)) 5)))                           (* -1. (cos (* 4. s))))))))  (entmake (list (cons 0 "SEQEND")))  (princ))`
Enjoy!

JCTER

• Guest
Re: Fractal Fun
« Reply #47 on: November 19, 2009, 09:36:53 AM »
there we go.  This is more along the lines of where I was hoping to go.

JCTER

• Guest
Re: Fractal Fun
« Reply #48 on: November 19, 2009, 10:42:36 AM »
Code: [Select]
`Had an idear.  I have no software to triangulate a surface from a given point grid, but it might come out interesting if someone does.I've modified the code shown below to also provide a Z variation of the points based upon iteration, similar to how it gets the color.  Forgive me if I did not place the added bits in the most elegant or proper position for the intent I tried to accomplish... I'm very amateur.[code](defun c:jfract (/ iLim xMin xMax yMin yMax xInc yInc x y [color=red]z zFac [/color]a b i)  (vl-load-com)  (setvar "PDMODE" 0) (setvar "PDSIZE" 0)    (setq iLim 255  ;; Iteration Limit        xMin -0.3 xMax  0.7  ;; Image Size        yMin -0.2 yMax  0.3        xInc 0.005 yInc 0.005 ;; Resolution        Re[c] -0.8   ;; Real Coefficient of Julia Constant        Im[c] 0.156  ;; Imaginary Coefficient of Julia Constant [color=red] zFac 0.05    ;; Elevation range modifier[/color]        )   (setq x (- xMin xInc))  (while (<= (setq x (+ x xInc)) xMax)        (setq y (- yMin yInc))    (while (<= (setq y (+ y yInc)) yMax)      (setq i 0 a x b y) ;; Julia      (while (and (< (norm a b) 4.)                  (<= (setq i (1+ i)) iLim))[color=red] (setq z (* (* i (/ (+ xInc yInc) 2)) zFac))[/color]        (setq new (z^2 a b) a (+ (car new) Re[c]) b (+ (cadr new) Im[c])))      (pnt (list x y [color=red]z[/color]) (rgb (* i 1) ;;;;; red (* i 1) ;;;;; green (1+ (rem (expt 1.1 i) 255)))))) ;;;;; blue  (princ))(defun pnt (pt col)  (entmakex    (list (cons 0 "POINT") (cons 10 pt) (cons 420 col))))(defun norm (x y)  (+ (* x x) (* y y)))(defun z^2 (x y)  (list (- (* x x) (* y y)) (* 2 x y)))(defun rgb (r g b)  (+ (* 65536 r) (* 256 g) b))`

Code: [Select]
`[color=red] (setq z (* (* i (/ (+ xInc yInc) 2)) zFac))[/color]`
To explain what I was doing here...

I basically wanted the iterative number to also cause a variation in the Z axis, similar to how the iterative number causes a variation in the color value.  I also wanted the Z variation to kind of logically match the size/scale/density of the image you're trying to produce, so I incorporated the average of the xInc and yInc values multiplied by the iterative number.  I'm testing how this works on a variety of xInc/yInc values to see if it works as I intended.  Given that the Z value was going to be 0-255 (I think, since it's based on i) I knew that the Z variation would need to be scaled down for a more logical 'terrain' showing... thus I multiple the whole thing by the new variable "zFac" which is set to 0.05 in the above code.

I don't have any software that includes a "DRAPE" tool, or any surface triangulation tools, and even if I did, considering that some of our fractals have upward toward 1,000,000 points, I am not so sure it would be possible to do so... but it still makes for some fun imagery. [/code]

Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #49 on: November 19, 2009, 11:19:50 AM »
Nice one James - nice idea about using the Z-Coord

JCTER

• Guest
Re: Fractal Fun
« Reply #50 on: November 19, 2009, 02:32:27 PM »
SW ISO view with the plan view beside it.

This is fun... you got me a little obsessed now LeeMac  Thanks for the toys.

Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #51 on: November 19, 2009, 03:08:54 PM »
Wow that is a little weird James! Not what I would have expected at all... I would love to be able to create the Mandelbulb, as shown in a previous link..

They are a little addictive though.. just trying different variations and waiting of the surprise of what is going to appear!

JCTER

• Guest
Re: Fractal Fun
« Reply #52 on: November 19, 2009, 03:17:54 PM »
Wow that is a little weird James! Not what I would have expected at all... I would love to be able to create the Mandelbulb, as shown in a previous link..

They are a little addictive though.. just trying different variations and waiting of the surprise of what is going to appear!

After looking at it, my first thought was "Hey, that's familiar!" and reminded me of: http://www.theswamp.org/index.php?topic=22296.0

Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #53 on: November 19, 2009, 03:31:45 PM »
I can see why a triangulation would be good, looking at Daniel's image

T.Willey

• Needs a day job
• Posts: 5231
Re: Fractal Fun
« Reply #54 on: November 23, 2009, 01:44:34 PM »
Lee,

Maybe you should check out this thread.  I knew there was one already, but couldn't find it earlier.

[ http://www.theswamp.org/index.php?topic=17746.0 ]
Tim

I don't want to ' end-up ', I want to ' become '. - Me

Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #55 on: November 23, 2009, 01:56:52 PM »
Lee,

Maybe you should check out this thread.  I knew there was one already, but couldn't find it earlier.

[ http://www.theswamp.org/index.php?topic=17746.0 ]

Wow! Tim you just made me feel so inadequate in comparison to that guy!   :ugly:

T.Willey

• Needs a day job
• Posts: 5231
Re: Fractal Fun
« Reply #56 on: November 23, 2009, 02:12:38 PM »
Lee,

Maybe you should check out this thread.  I knew there was one already, but couldn't find it earlier.

[ http://www.theswamp.org/index.php?topic=17746.0 ]

Wow! Tim you just made me feel so inadequate in comparison to that guy!   :ugly:

We are all learning to some extent.  Don't worry.  You have passed me way by with this.
Tim

I don't want to ' end-up ', I want to ' become '. - Me

JCTER

• Guest
Re: Fractal Fun
« Reply #57 on: November 23, 2009, 02:45:26 PM »
DANG! I had this set to run over the weekend... got it to zoomALL, for the screenshot, but I did a VIEW command to hit the SEI view, to show the variance in the Z elevation... and AutoCAD CRASHED!!!  :realmad:  It also failed to save the drawing for recovery, so I couldn't get it back

I'm going to try again tonight, and set the density slightly smaller to help.  Here's the SS anyhow...

Lee Mac

• Seagull
• Posts: 12350
• London, England
Re: Fractal Fun
« Reply #58 on: November 23, 2009, 02:53:03 PM »
Wow! that is nice James

But be careful about the memory limitations of AutoCAD... you are probably generating a few million points here..

JCTER

• Guest
Re: Fractal Fun
« Reply #59 on: November 23, 2009, 02:55:47 PM »
Yea, I know, I keep pushing the envelope a bit.

I just want to get a decent DWG with the Z-effect done as I wanted... and then find some sort of triangulation routine.