Print Page - Brand New fractal type

Title: Brand New fractal type
Post by: M Benesi on May 21, 2010, 07:27:23 AM

  Basically, I resurrected an old failed formula of mine and applied knowledge recently applied to another old formula: multiply x,y,z (vs. yz, xz, xy) values by negative rotations - 1 (for z^3 multiply by -4) and multiply the new x, y, and z values by 3 (magic) before adding in pixel values.

However, mess with the multipliers (based off rotation values) if you find that the system is not producing interesting images: for example, the z^17 fractal might not produce interesting images with a multiplier of -18, however using a multiplier of -3 produces a fractally, albeit spiky, object. I've found that using a multiplier of -1 gives good, but spiky fractals for z^n > ~9 (yeah... I know, should have checked to see if sign reversal worked first.. I did, so you know, but with the z^2 variety you don't get great fractallyness for multipliers that low: I prefer -2.5 to -3 for that fractal, until I find out something new). Anyways, I've yet to find a pleasing multiplier for z^7, although somewhere around -8 seems good enough. Need to figure out another method of multiplier assignment... or do abs(sx) *sx method of calculations.

  Anyways, it seems that a value around 2.6-2.7 works best for the z^2 version (it gives far more interesting outcroppings on the one side) so.. further experimentation is needed. for z^3 ~ 3.7 . etc..

  Here is the ChaosPro code (minus a few unnecessary, possibly confusing modifications that I play with):

Code:

  //Copyright Matthew Benesi, per the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 Unported License
  (http://creativecommons.org/licenses/by-nc-sa/3.0/)

         r=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
	 phi=atan2(sx*scalef+flip (sqrt(sqr(sy)+sqr(sz))));       // [s]scale of 3 makes it work nice[/s]
	 tango=atan2(sy*scalef+flip(sqrt(sqr(sx)+sqr(sz))));   // scale of - rotations + 1 seems best (for z^3  scalef=-4, z^9 scalef=-10)
	 whiskey=atan2(sz*scalef+flip(sqrt(sqr(sx)+sqr(sy))));   //   - rotations doesn't alter evens (wondered why odds were wierd)
	
	nx=r*cos(phi*v)*check;                                           //  check of 3 makes it work nice
	ny=r*cos(tango*v)*check;     //perhaps you noticed that I scavenged variables from another formula....   :D
	nz=r*cos(whiskey*v)*check;
	
	
	if (juliaMode) {
	    sx=nx+cr;  // same as below: values for x y and z
	    sy=ny+ci;
	    sz=nz+cj;
	
	} else {
	    sx=nx+pixelr;   // pixelr is the x value of the pixel, pixeli the y, pixelj (guess... z?)
	    sy=ny+pixeli;
	    sz=nz+pixelj;
	
	} 
	bail =sqr(sx)+sqr(sy)+sqr(sz);       //this is my bailout check variable... the term bailout is already used (I think) so I use bail

  Phenomenal results. The z^2 version is amazingly fractal. I skipped a few z^n and went to z^13 (good number: odd, plus lots of details.. or so I assumed and found out). There are interconnected areas within the fractals: pillars, loops, Mandelbulbesque pillars, hills, and places to explore. So first off are a few z^2:

Top view (there are 2 of these, then 2 back views, in other words, it can be rotated 90 degrees once and end up the same, then again and it is different, then again it is the same, once more you are back at the first/second (unless you rotated to the other image first... bleh))
(http://lh5.ggpht.com/_gbC_B2NkUEo/S_YVD2H_YXI/AAAAAAAAAN4/9wpr6lfWFPY/front%20large.jpg)
Random zoom in from top (I turned 45 degrees to look at a structure after zooming between some things, then zoomed and iterated a bit (13?)):
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_YVEKvjIhI/AAAAAAAAAN8/XrfNyPQs2wk/some%20random%20zoom%20turned%20around.jpg)
this one I had a certain setting changed (set newxyz multiple to 4 instead of 3, not necessary to do so... so will have to find it again without screwed up settings):
(http://lh4.ggpht.com/_gbC_B2NkUEo/S_YVEXn4cvI/AAAAAAAAAOA/YL1_sW7j2Hk/pillars%20of%20creation.jpg)
this is a back shot. The back is pretty boring... at least where I looked. It is fractal... but... repetitive (unless maybe a different angle?)
(http://lh5.ggpht.com/_gbC_B2NkUEo/S_YVDqywpRI/AAAAAAAAAN0/Ktn-iFwKABE/back%20or%20something%20large.jpg)

  That's it for the z^2s. Now the z^13s, 2 800x800, then a bunch of small ones (I was exploring the new formula, don't worry Trifox, they are in my picasa album):

  So this one is an 800x800 zoom into 45 degrees off the squarish section of the z^13. I zoomed in on a couple of the bulbs (well, flat bulbs, there are regular bulbs, spiky bulbs, bulbs with a spiral of bulbs going up them, etc.):
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_YVEtRyuzI/AAAAAAAAAOE/Zl7ZWUN-bhA/zoom%20on%20spikes%20big.jpg)

This is an 800x800 zoom between the bulbs (color changed to green, but it's between the ones in the image above, perhaps the central and the one above it, then I rotated towards the one above it and zoomed into it a bit, added shadows to show a bit more details):
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_Ybr_uBr7I/AAAAAAAAAOI/pR-bQLxqpGc/between%20flat%20bulbs%2C%20zoom%20on%20one%20of%20them%20shadowed.jpg)

  Here are a few small ones, first one of the spiky forest bulbs:
(http://lh4.ggpht.com/_gbC_B2NkUEo/S_Ybsf3IRcI/AAAAAAAAAOM/1wuzfx5dr9U/fractal%20forest%20zoom%20on%20one%20spike.jpg)
bad shot, zoomed between the bulbs into the loops and went upside down, increased iterations, not big enough, but here it is anyways:
(http://lh5.ggpht.com/_gbC_B2NkUEo/S_Ybssg8o7I/AAAAAAAAAOQ/Qc4HTVjVj2Y/zoom%20between%20loops%20between%20spikes.jpg)
This is just to show the variety of shapes of the main spikes/bulbs. Some flat, some round, some pointy. And there are other sections (not necessarily as awesome):
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_Ybs13EPkI/AAAAAAAAAOU/SyVSml49GNQ/45%20degree%20view%20to%20show%20variety%20of%20spikes.jpg)

Title: Re: Brand New fractal type
Post by: Timeroot on May 21, 2010, 07:44:17 AM

i LIKE! ;D ;D ;D

Title: Re: Brand New fractal type
Post by: M Benesi on May 21, 2010, 07:54:47 AM

Woo!

Title: Re: Brand New fractal type
Post by: reesej2 on May 21, 2010, 08:55:37 AM

Wow, very nice! Beautiful.

Title: Re: Brand New fractal type
Post by: visual.bermarte on May 21, 2010, 01:20:12 PM

So nice..it would be fun to have a version made using hlsl or similar.

Title: Re: Brand New fractal type
Post by: M Benesi on May 23, 2010, 09:06:11 AM

Thanks reesej and visual.

Here are a few more images, with the improved formula (scalef = - rotation multiplier -1: if rotation multiplier is 3 (for z^3), set scalef variable to -4).

2nd order pillars:
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_jSS2aiHBI/AAAAAAAAAOg/Et8kl3ISeYU/crystal%20pillar%20color%20change%20light%20goof.jpg)
(http://lh5.ggpht.com/_gbC_B2NkUEo/S_jSTIwgYAI/AAAAAAAAAOk/SLHND4-k5cA/crystal%20pillar%20zoom%20in%20on%20middle%20pillar%20increased%20iterations%20light%20change.jpg)

4th order large bulb (main large bulb):
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_jSTWSs4mI/AAAAAAAAAOo/4SpcKfkWlyY/quarter%20top%20shot.jpg)

4th order zoom into large bulb (somewhere):
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_jSSjfrt_I/AAAAAAAAAOc/bIUZvl0EBao/nice%20shot.jpg)

9th order zoom straight in (between little bulbs arranged in a square pattern, holes due to clipping, left them in because they show the structure behind the first layer of fractally goodness):
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_jST14PGFI/AAAAAAAAAOs/gFwc4CZ29VQ/zoom%20straight%20down.jpg)

Title: Re: Brand New fractal type
Post by: Sockratease on May 23, 2010, 09:55:30 PM

Quote from: M Benesi on May 21, 2010, 07:27:23 AM

fractallyness

Love that word! Guess that means I have Fractallynessophilia!

And the images are impressive too :D

I'll be plugging it in to ChaosPro for a play when this entry for a 3D Art contest finishes rendering...

Title: Re: Brand New fractal type
Post by: M Benesi on May 24, 2010, 07:51:32 AM

Sockratease: I didn't include the variable assignments, as the code is in my "play around with fractal formulas" codebase, which has TONS of variables from various fractal types.

   If you need, I can post some "real" code, instead of the truncated version above. It's simply there to show the formula. For now, here is a new image from a related formula (actually, the first satisfactory implementation of this formula was the second real hybrid with the MandelBox: Amazing Hybrid D), after a brief explanation:

  The first implementation of Amazing Hybrid D used code from my original Type D fractal, which was boring. Type D is totally boring. However, blending it with the box made it sortof interesting, and increasing it to 4 dimensions added a slight bit of versatility/variation (lots of compute cycles though). Well, the 3d and 4d version of the Amazing Hybrid D didn't include the scalar multiplier in the atan2 statement that the new Type DUH (Type D Uber Haxored) fractal uses to achieve full fractallyness. So... The new Amazing Hybrid DUH (Amazing Hybrid D Uber Haxored) is simply the same code with a scalar multiplier to correct the lack of scalar multipliers in the original formula. In other words, it's been UHed.

  Here is an image from the new implementation, with a correct (by correct, I mean I like it for now) scalar multiplier (what I feel is correct for z^3 is ~3.7). It has all these cute little heart things, making the fractal slightly ahem, as it's the first fractal my girlfriend saw from far away and said "ohh, that's pretty", which basically ruins my dark designs on introducing evil fractals to the universe. Or does it? More follows.

  Here is the image:
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_oQQ2sEBsI/AAAAAAAAAO8/l9osxlUlKMI/straight%20on%20hearts.jpg)

And here is the more:
(http://lh5.ggpht.com/_gbC_B2NkUEo/S_oaSPaeALI/AAAAAAAAAPM/cqDFd40otg8/demon%20head%202.jpg)
brighter...:
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_oaR5O16NI/AAAAAAAAAPI/4-_Zl4_8YPU/demon%20head%204.jpg)
Central Chamber... Arkenstone?
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_oaRn4WXVI/AAAAAAAAAPE/iqVUbmQSVh8/central%20chamber%202.jpg)

Title: Re: Brand New fractal type
Post by: kram1032 on May 24, 2010, 09:49:52 AM

Well, I have to admit, to me the ahemish render it the most beautiful of them. I guess, it's because of the colouring used though^^
The second one doesn't look that unevil ;)

In the third one, I really don't like the colour sheme but else, it's nice too :)

Title: Re: Brand New fractal type
Post by: Jesse on May 24, 2010, 04:56:13 PM

Interesting new shapes, as always!
Talking about the math, i feel you are thinking some dimensions higher than me :)

Quote from: M Benesi on May 24, 2010, 07:51:32 AM

It has all these cute little heart things, making the fractal slightly ahem, as it's the first fractal my girlfriend saw from far away and said "ohh, that's pretty", which basically ruins my dark designs on introducing evil fractals to the universe. Or does it? More follows.

Hmm, thats the thing, you never know what you find. Some were to offending to show them.
Hope that this evil fractal can be shown, land of the damned:

Title: Re: Brand New fractal type
Post by: M Benesi on May 24, 2010, 09:48:18 PM

Jesse, lol... I'm getting a peaceful vibe off of "The Land of the Damned".

kram1032- I think she said it had to do with the coloring as well. The complexity of the fractal (variations in distance from point 0,0,0) causes interesting variations in the color scheme (assigned by distance from point 0,0,0).

As to the second one, yeah. It has a slightly demonic looking face in it. Or maybe that's just my wishful thinking at play. As to the third... I need to learn to color. If I was in charge of the universe, everything would be purple, green, gold, silver, and black.

Or these bad colors. Anyways, Amazing Hybrid DUH is related to type DUH... so I'll post these next 2 hybrid images, working on an interesting (to me) z^2 type DUH 1000x1000 render which should be done in a couple hours that will be put in the thread later (or in this message later).

(http://lh5.ggpht.com/_gbC_B2NkUEo/S_rUyzpzmiI/AAAAAAAAAPU/awmEaypzADw/maelstroms%20crown.jpg)
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_rUy58pGwI/AAAAAAAAAPY/3-ef1159vog/space%20alien%20tower%20structure.jpg)

Title: Re: Brand New fractal type
Post by: kram1032 on May 24, 2010, 10:11:21 PM

Quote from: M Benesi on May 24, 2010, 09:48:18 PM

Amazing Hybrid DUH is related to type DUH.

D'uh!

Sorry, couldn't resist xD

Well, especially green and violet hardly fit togehter in most cases. (Although various purple flowers proof this wrong. However, both the used purples and shades of green differ a lot from what you do there ;) )

And yup, the demonic face is, what makes the second one evil :)

Title: Re: Brand New fractal type
Post by: Jesse on May 24, 2010, 10:23:11 PM

Quote from: M Benesi on May 24, 2010, 09:48:18 PM

Jesse, lol... I'm getting a peaceful vibe off of "The Land of the Damned".

Must be the coloring :)

Do you have some code snippet from the last image?

Title: Re: Brand New fractal type
Post by: M Benesi on May 26, 2010, 05:57:37 AM

Quote from: kram1032 on May 24, 2010, 10:11:21 PM

Quote from: M Benesi on May 24, 2010, 09:48:18 PM

Amazing Hybrid DUH is related to type DUH.

D'uh!

Sorry, couldn't resist xD

:D The "DUH" name is in honor of my grandfather, who says "Duh" to me when I said something completely obvious, or something completely oblivious... one of the two. Makes me laugh to think about it. As to the other thing... color coordination is not my strong suit. I like black.

Title: Re: Brand New fractal type
Post by: M Benesi on May 26, 2010, 06:55:23 AM

Quote from: Jesse on May 24, 2010, 10:23:11 PM

Quote from: M Benesi on May 24, 2010, 09:48:18 PM

Jesse, lol... I'm getting a peaceful vibe off of "The Land of the Damned".

Must be the coloring :)

Do you have some code snippet from the last image?

First, rename "benesi fractals.txt" to "benesi fractals.cfm".
  Next you'll have to drop this non-edited version of benesi fractals.cfm into your ChaosPro formula directory, not the benesi subdirectory (by non-edited I mean it has a lot of incomplete formulas- never finished the 6d.. don't think I got too far in the 5d versions, some random experiments in the other subsets). Also, rename the parameter file from .txt to . (no extension). I don't know if you have to do so, but my parameter files never have extensions, but can't attach it here without an extension.

  The image is from the new "Amazing Hybrid D 4d" formula with sscale as a multiplier. If you want to change the z^n value, you need to change linear rotations, linear magnitude, planar rotations set equal to eachother, and set sscale = - linear rotations - ~ 1 (for z^2 sscale ~-3 for z^5 sscale ~-5.5 or -5 for z^9 sscale ~-9).

  The "Play around with fractals" set has "type doy" (the original name for type duh, but I don't feel like editing all of the parameter files so left it at that.. for now) and a bunch of random formulas, some of which need certain setting to achieve anything, some I think are rather... boring.

  Now, the "play around with fractals" subset has a BUNCH of boolean settings in it (check boxes). For the version of "type duh" (formula doy in the drop down menu) I think is... "correct" check the "exp3" box (stands for experiment 3). Play with the other settings if you like (does some freaky stuff, nothing that great, but maybe you will find something amazing... I don't know). The newer version of type duh (exp3 checked) works well with scalef set = linear rotations + ~1 = linear magnitude +~1 (so for z^2, set scalef = 3, for higher z^n I set it equal to the number of rotations, so z^5 scalef= 5.5, z^9 scalef=9).

  There are a lot of parameters that aren't used in type duh, so you don't have to change them. You can set check to 3 (I like 3... not necessary, but I like it, it should be around 1-4 so I don't have to explain lots of stuff) to mess around with the fractals.

  Good luck. :D

Title: Re: Brand New fractal type
Post by: M Benesi on May 26, 2010, 07:31:27 AM

Here is something from the new "exp3" version of type duh, really shows the pattern of the fractal. I should mention that I implemented this as an option in 4d Amazing Hybrid D as "absmode" switch... and it gives cool new patterns. I'll reupload the cfm file in the above reply to Jesse so that people can play with that.

Code:

r=(sqr(sx)+sqr(sy)+sqr(sz))^(n/2);
phi=atan2([b]abs(sx)[/b]*scalef+flip (sqrt(sqr(sy)+sqr(sz))));   //  used the absolute values of x,y,z instead of signed x,y,z
tango=atan2([b]abs(sy)[/b]*scalef+flip(sqrt(sqr(sx)+sqr(sz))));
whiskey=atan2([b]abs(sz)[/b]*scalef+flip(sqrt(sqr(sx)+sqr(sy))));

Anyways, a series of 333x333 images. z^2 through z^6. You should see the pattern: total number of bulbs= n^2 of z^n, so there are 4 for z^2, 9 for z^3, 16 for z^4..... Just the 4 main ones for z^2...

(http://lh6.ggpht.com/_gbC_B2NkUEo/S_yqgal0YBI/AAAAAAAAAPw/q8Wh_QnXMIg/2nd.jpg)(http://lh5.ggpht.com/_gbC_B2NkUEo/S_yqgXfX0mI/AAAAAAAAAP0/4khwChu52hk/3rd.jpg)(http://lh5.ggpht.com/_gbC_B2NkUEo/S_yqgnbmRpI/AAAAAAAAAP4/_liSan_uneU/4th.jpg)(http://lh6.ggpht.com/_gbC_B2NkUEo/S_yqhCvBPDI/AAAAAAAAAP8/2B0lUYPkdMI/5th.jpg)(http://lh5.ggpht.com/_gbC_B2NkUEo/S_yqhAsgF5I/AAAAAAAAAQA/0yM2NGVIha4/6th.jpg)

Then here is a nice z^5 amazing hybrid d 4d (with sscale=-5.5) straight on shot:
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_yqXBJWzuI/AAAAAAAAAPk/hwVaXFnPSsw/straight%20on.jpg)

Title: Re: Brand New fractal type
Post by: M Benesi on May 28, 2010, 07:14:12 AM

Anyways, new code below. It works perfectly, eliminated a few variables, will be easier to analyze mathematically when I send it off to various smart people.

Allright, I found out that the other new fractal type I posted works better to generate the same fractals (just changed the code a bit). Anyways, a brief explanation:

I set fold to .5 (for all z^n), scalef to -3 for odds, 3 for evens (unless you want to rotate the fractal 180 degrees... that's up to you, I prefer changing the sign... as I'm already altering another variable), check=rotations=magnitude exponent (works for them all, but you can mess around with other variations). Gets boring for higher n value z^n: fractal flattens out, except you can mess with the straight on pegs (those are pretty neat, go down between them, turn towards one, turn away from fractal a bit but facing peg and look at structure of peg). You can always mess around with settings and find spiky versions of the fractal as well, but they aren't as pleasing (to me).

Side note: the amazing hybrid version of this is pretty phenomenal. Way out there. But I had this to play with today.... the amazing hybrid version should make it to the thread soon, then both of these will be put into the next Benesi set update in the ChaosPro formula database. Pretty busy today.... should be out soon (I've already played with it, need to simplify/clean up code)

Code:

  Simplified code (you can't mess around as much, but it works perfectly):

   In your initialization area (not iterative loop) do this:

checkvar = n * sqrt (2);

  If you're using ChaosPro and putting this formula into the Benesi Set "play around with fractals" subset (writing over
 the old mag vs xyz fractal type) use this string in the initialization area after adding the [b]real[/b] [i]checkvar[/i] to
 your variables list (or use another pre- existing variable (instead of making the new variable checkvar) not used in the
 fractal already-DO NOT USE A PARAMETER!!! (overflows can occur))):

     if (fractaltype=="mag vs xyz") {
        checkvar=n*sqrt(2);
	}

   You do it in initialization so you don't have to keep taking the square root of 2 each iteration of the loop. 

loop:

	r= sqrt (sqr(sx) + sqr(sy) + sqr(sz));  
	r2= r^n; 

	theta=atan2 (abs(sx) * checkvar + flip(r));   /* calculated checkvar in initialization before loop */
	phi=    atan2 (abs(sy) * checkvar + flip(r));  /* using the absolute value of the x, y, and z components gives a much */
	tango=atan2 (abs(sz) * checkvar + flip(r));  /* nicer fractal (in my opinion)*/

	nx= r2 * cos (theta * n);  
	ny= r2 * cos (phi *    n);    
	nz= r2 * cos (tango * n);

	if (juliaMode) {
	sx= nx + cr;
	sy= ny + ci;
	sz= nz + cj;

	} else {
	sx= nx + pixelr;
	sy= ny + pixeli;
	sz= nz + pixelj;

}

	z = quaternion (sx,sy,sz,0);   /* lets you use orbital coloring.. didn't know that until today.. */
	bail = sqr (sx) + sqr (sy) + sqr (sz);

That's the code... here are a couple of images, same as the other fractal formula, just works better, less messing around finding "the right check/scalef combination". It's a tighter fractal... works a lot better.

z^2 main fractal, a tiny bit zoomed:
(http://lh4.ggpht.com/_gbC_B2NkUEo/S_9nQcp3FpI/AAAAAAAAAQo/BBfAAxwX2h4/straight%20on%20big.jpg)
z^3 one of the 4 outcroppings:
(http://lh6.ggpht.com/_gbC_B2NkUEo/S_9MAe6JIdI/AAAAAAAAAQc/SN62eteiKxA/awesome%20colors.jpg)
z^5 zoom into one of the 4 outcroppings (main outcroppings, 4 corners of fractal):
(http://lh3.ggpht.com/_gbC_B2NkUEo/S_9MAjvh1zI/AAAAAAAAAQg/vhanrsIVP0Q/nice%20shot.jpg)

z^5 with abs of x,y,z in angle calculation:
(http://lh6.ggpht.com/_gbC_B2NkUEo/TAAQcSnw8cI/AAAAAAAAAQw/T2VnnYpFUQY/quick%20zoom%20on%20top.jpg)

Title: Re: Brand New fractal type
Post by: Jesse on May 28, 2010, 11:41:54 PM

Thank you for the code, 6 dimensions are too much for my little pogram, the last one looks better :dink:

Cant say if i ever find the time for testing :sad1:

Title: Re: Brand New fractal type
Post by: Nahee_Enterprises on May 29, 2010, 01:22:39 AM

Quote from: M Benesi on May 26, 2010, 06:55:23 AM

   First, rename "benesi fractals.txt" to "benesi fractals.cfm".
   Also, rename the parameter file from a .txt to .(no extension).
  I don't know if you have to do so, but my parameter files never have extensions,
but can't attach it here without an extension.

First off, thank you for supplying the attached formula and parameter files. :)
Secondly, usually parameter files have a .PAR file extension. And this forum is setup to handle such file types.

Title: Re: Brand New fractal type
Post by: Nahee_Enterprises on May 29, 2010, 01:26:30 AM

Quote from: M Benesi on May 26, 2010, 07:31:27 AM

Here is something from the new "exp3" version of type duh.....

Then here is a nice z^5 amazing hybrid d 4d (with sscale=-5.5) straight on shot:
lh3.ggpht.com/_gbC_B2NkUEo/S_yqXBJWzuI/AAAAAAAAAPk/hwVaXFnPSsw/straight%20on.jpg

I really like the way this last image turned out!!!! Very Nice !!!! :)

Title: Re: Brand New fractal type
Post by: M Benesi on May 29, 2010, 09:24:02 PM

Thanks, it's just a straight on shot of Amazing Hybrid D 4d with rotations and magnitude set to 5 and scheck set to -5.5. I'll attach an updated set of formulas (just replace the updated set in the formulas directory of ChaosPro).

  I'm removing the sloppy non-edited set that's on the previous page (too many variables... etc.) and replacing it with the formula set I am posting in the ChaosPro database. You will find the new corrected "mag vs xyz" formula under the "Benesi Set" subset, and the various hybrids under the "Tom Lowe's Mandelbox and Benesi's variations" formula subset.

  Amazing Hybrid G is the "corrected" formula that uses the newest variation of the magnitude vs linear (x, y, and z) formula (the formula with checkvar= scheck*sqrt(2)). Just set rotations=magnitude=scheck (or set scheck= -rotations) to get something nice.

  Or to play with the other hybrid formulas: use negative scheck values that are a little larger in magnitude than rotations (for 2 rotations use scheck ~-3 for 5 rotations use ~-5.5, dropping down to ~-9 for 9 rotations). Or you can use positive scheck values for different structures (try 3 for various rotation values, it makes neat patterns).

  Adding a bunch of Hybrid G shots (4d for most):

z^2 top corner, absmode:
(http://lh5.ggpht.com/_gbC_B2NkUEo/TAHxxVNSZ0I/AAAAAAAAARE/YTBrbz2IQoQ/135%20shot.jpg)
z^3 (might be z^4 or 5.. dunno) top corner, ?maybe absmode?:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TAHxxu3LulI/AAAAAAAAARI/BnOP26Bdqds/n135%20n3%20abs%20corner.jpg)
z^4 top corner (-135 rotation or 45.. forget) pillars, one more iteration for the second one:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TAHxx7OzWZI/AAAAAAAAARQ/x3Xc1cr2tVA/top%20pillar%20n135%20rot.jpg)
(http://lh6.ggpht.com/_gbC_B2NkUEo/TAHxx7Cpg6I/AAAAAAAAARM/nVW2oNNUxi4/pillar%20more%20iterated.jpg)

  Now for the 4d shots. I set times to 0, .25, .5, .75, and 1 for this series of z^3 shots:
(http://lh5.ggpht.com/_gbC_B2NkUEo/TAHxyPNHK0I/AAAAAAAAARU/UfpN7Cz0HGI/time%200.jpg)
(http://lh5.ggpht.com/_gbC_B2NkUEo/TAHzdxuw-PI/AAAAAAAAARc/RO_wsk2iWyc/time%20p25.jpg)
(http://lh5.ggpht.com/_gbC_B2NkUEo/TAHzeLIbZNI/AAAAAAAAARg/CQXlh5AH-fk/time%20p5.jpg)
(http://lh3.ggpht.com/_gbC_B2NkUEo/TAHzevLvYFI/AAAAAAAAARk/fb2sfTW6IE4/time%20p75.jpg)
(http://lh5.ggpht.com/_gbC_B2NkUEo/TAHzehEFBpI/AAAAAAAAARo/l_bjimbCKcI/time%201.jpg)

  This next series is a zoom into the top corner (I call it the top corner, but I'm not sure if I rotated it -135 degrees or 45 degrees...), some iteration increases, although as with regular Mandelbox, you get swiss cheese effects if you don't zoom in enough (or use insanely high resolutions that take a billion years to calculate):
time 0, same iterations.. maybe. don't recall. maybe increased by one?
(http://lh6.ggpht.com/_gbC_B2NkUEo/TAHze1bRsVI/AAAAAAAAARs/1oUnY3wvKCo/time%200.jpg)
time .25:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TAH0mS6UhAI/AAAAAAAAAR8/OOHaluRTBOY/time%20p25.jpg)
time .5:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TAH0mqnAFVI/AAAAAAAAASA/oEuGrbRDeIQ/time%20p5.jpg)
time .75:
(http://lh4.ggpht.com/_gbC_B2NkUEo/TAH0mw2jaVI/AAAAAAAAASE/_RBd6jdZ2Ys/time%20p75.jpg)
time 1:
(http://lh5.ggpht.com/_gbC_B2NkUEo/TAH0m6jowXI/AAAAAAAAASI/ruwCCXbonQo/time%201.jpg)
time .25 1 more iteration:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TAH7eLWxJKI/AAAAAAAAASQ/Y3rDpA-6RCA/time%20p25%20more%20iterations.jpg)
time .75 1 more iteration:
(http://lh3.ggpht.com/_gbC_B2NkUEo/TAH7edFMvYI/AAAAAAAAASU/CTUOHskQV_c/time%20p75%20more%20iterations.jpg)

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Fractal Art => Images Showcase (Rate My Fractal) => Topic started by: M Benesi on May 21, 2010, 07:27:23 AM