Brand New fractal type

[M Benesi]

  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...   



  Then here is a nice z^5 amazing hybrid d 4d (with sscale=-5.5) straight on shot:

[M Benesi]

  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:

z^3 one of the 4 outcroppings:
  
z^5 zoom into one of the 4 outcroppings (main outcroppings, 4 corners of fractal):


z^5 with abs of x,y,z in angle calculation:

[Jesse]

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

Cant say if i ever find the time for testing 

[Nahee_Enterprises]

    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.
 

[Nahee_Enterprises]

    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 !!!!   
 

[M Benesi]

 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:

z^3 (might be z^4 or 5.. dunno) top corner, ?maybe absmode?:

z^4 top corner (-135 rotation or 45.. forget) pillars, one more iteration for the second one:



  Now for the 4d shots.  I set times to 0, .25, .5, .75, and 1 for this series of z^3 shots:






  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?

time .25:

time .5:

time .75:

time 1:

time .25 1 more iteration:

time .75 1 more iteration: