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Author Topic: Quadray Sets  (Read 24457 times)
Description: Quadray representations of the mandelbrot set
0 Members and 2 Guests are viewing this topic.
Aexion
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The Fractal Hermit


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« Reply #60 on: May 06, 2011, 11:24:22 AM »

The SnowFlake of Diamonds
Here is another 4D experiment. It's not a Quadray, but it produces interesting results.
This consists in a modified mandelbox that runs on an hexagonal (actually triangular) configuration.
At delta=0, it produces an interesting array of snowflake. Around delta=7, it breaks down into six triangles.
I also changed a bit the original mandelbox, so instead of producing arches and cupolas, it produces crystaline structures.



Init Conditions:
Code:
const float delta=0;
const float ctx =fabs(z)-delta;
const float cty =fabs(0.86602540378443864676372317075294*x-0.5*z)-delta;
const float ctz =fabs(-0.86602540378443864676372317075294*x-0.5*z)-delta;
const float ctw =fabs(y)-delta;
x=0;
y=0;
z=0;
float w=0;

Iteration Loop:
Code:
for (ic=0;ic<Iter;ic++){
if(x>1)x=2-x;
else
if(x<-1)x=-2-x;
if(y>1)y=2-y;
else
if(y<-1)y=-2-y;
if(z>1)z=2-z;
else
if(z<-1)z=-2-z;
if(w>1)w=2-w;
else
if(w<-1)w=-2-w;

const float vm=fabs(x)+fabs(y)+fabs(z)+fabs(w);//sqrt(x*x+y*y+z*z+w*w);

if(vm<0.05){
x=x*4;
y=y*4;
z=z*4;
w=w*4;
} else
if(vm<1.5){
const float vsq=vm*vm*vm;
x/=vsq;
y/=vsq;
z/=vsq;
w/=vsq;
}
x=2*x+ctx;
y=2*y+cty;
z=2*z+ctz;
w=2*w+ctw;

if ((x*x+y*y+z*z+w*w)>3600) break;

}
 
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Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
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Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #61 on: May 06, 2011, 11:56:42 AM »

 smiley Excellent!!!! Big thanks friend!!! angel I am only wondering if it works leaving unchanged x axis, and rotating others...

For example;

const float ctx =fabs(x)-delta;
const float cty =fabs(0.86602540378443864676372317075294*y-0.5*x)-delta;
const float ctz =fabs(-0.86602540378443864676372317075294*y-0.5*x)-delta;
const float ctw =fabs(z)-delta;

Or even better;

const float ctx =fabs(x)-delta; (x remains x)
const float cty =fabs(0.86602540378443864676372317075294*y-0.5*x)-delta;
const float ctz =fabs(z)-delta; (z remains z)
const float ctw =fabs(-0.86602540378443864676372317075294*y-0.5*x)-delta;

It can be much less "distructive" for the formula combinations, I will try smiley

Luca wink

-----------------

PS; No need to report Abox formula everytime, it is fixed and I know it cheesy
« Last Edit: May 06, 2011, 11:59:47 AM by DarkBeam » Logged

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DarkBeam
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Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #62 on: May 06, 2011, 12:55:50 PM »

 dance moves w00t !!

It works!!! I adopted my version with less axis swapping, works like a charm grin


* hexa.jpg (98.49 KB, 724x708 - viewed 575 times.)
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DarkBeam
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Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #63 on: May 06, 2011, 01:10:41 PM »



Warioland... Wanna enter? evil


Mandelbulb3Dv16{
O....Es....V1...w....2....EcjftkoxE3.HeVHx1SySzjFmAlH0Jctzvl/10CZxW/.7kKuVu82G/k
................................HYnyQn3Px.2........Y./..................y.2.....
................/ME//....6.90...70....E2.....caxON8IVIlD/..........c./...w1....U
z.....kD1E../..........wz........................................y1...sD...../..
.w1...sDP46P/2x7VwX4TjYavww2zUhzCWzweMZjME31SkW6Hw9CilHqA776z.mO3eAO/GkD0UxNSiUV
ovH6vYIa61Q.ze2BuPtSWAmD......Yp......................sD.2kz0...................
..............................MRS4.4qtN.kObb/UoRS4.srtN.sVbb/.FSS4..............
.....................Q4Kf0.U..6.P....A0...EF....U0...A0....F....8/...Y21...UJl2I
...U.0aZcv7M6/1eMg2cwX6dE16.0c..zrhe.cVoK/nl2xvjQvM93P58iz1...........U.8.UQgk0.
IwUmc2beYz1RdA8E5Exwz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................UTVR..y3q/.zz/k.1A..1Ak.szDsnwF.UDn
5/EzThdht0kaqa9.Qs5y3q/.sLM5..bTsLM5.UTVR..lyVTVR..y3q/.Mw5y3q/.sLM5.kqTsLM5.UTV
R..kzVTVR..y3q/....y3q/.zz/k.1A.yz1yAT2.xzpaqa9.................................
E....6....E.....I....2....kL6J4SVFZQVtqQaxaQh/..................................
...................wz.........zj................................................
................................................................................
.....................2.....3....4....2YEjVbJV7LSHBKMgJ4BY/......................
.Q...2..06U..........AnAnAnAnA.E........Uz1........wzUf53iSIsuuD........kz1.....
................................................................................
................................}
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Aexion
Conqueror
*******
Posts: 116


The Fractal Hermit


WWW
« Reply #64 on: May 06, 2011, 01:51:25 PM »

Nice render Luca....but you miss the chesse..look at the formula again.. cheesy
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Incendia for 3D Fractals
Aural for Musical Fractals
Kali
Fractal Supremo
*****
Posts: 1138


« Reply #65 on: May 06, 2011, 03:24:12 PM »

Good work, Aexion

I think I recall this part from somewhere:

Code:
fabs(x)+fabs(y)+fabs(z)+fabs(w);//sqrt(x*x+y*y+z*z+w*w)

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Aexion
Conqueror
*******
Posts: 116


The Fractal Hermit


WWW
« Reply #66 on: May 06, 2011, 03:54:43 PM »

Good work, Aexion

I think I recall this part from somewhere:

Code:
fabs(x)+fabs(y)+fabs(z)+fabs(w);//sqrt(x*x+y*y+z*z+w*w)



Oh.. Welcome to the world of the Manhattan Distance:
http://en.wikipedia.org/wiki/Taxicab_geometry

wink

Not always I follow Euclid cheesy (its the cause of the diamond like structures..)
(hmm..tell me, have you used it in your latest formulaes?)
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Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #67 on: May 06, 2011, 04:06:35 PM »

Nice render Luca....but you miss the chesse..look at the formula again.. cheesy

Chesse? What is? shocked

And I would like to use that bailout too, it seems to be useful kiss but how? undecided
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Aexion
Conqueror
*******
Posts: 116


The Fractal Hermit


WWW
« Reply #68 on: May 06, 2011, 04:12:21 PM »

Nice render Luca....but you miss the chesse..look at the formula again.. cheesy

Chesse? What is? shocked

And I would like to use that bailout too, it seems to be useful kiss but how? undecided

the difference between this formula and the standard mandelbox is:
Code:
const float vm=fabs(x)+fabs(y)+fabs(z)+fabs(w);//here.. its the manhattan distance instead of the euclidean one..

const float vsq=vm*vm*vm;// it's raised to the cube.. :)
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Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #69 on: May 06, 2011, 04:33:31 PM »

The problem is that I don't know how to control bailout, so this must be done by Jesse sad
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Kali
Fractal Supremo
*****
Posts: 1138


« Reply #70 on: May 06, 2011, 04:35:19 PM »

Good work, Aexion

I think I recall this part from somewhere:

Code:
fabs(x)+fabs(y)+fabs(z)+fabs(w);//sqrt(x*x+y*y+z*z+w*w)



Oh.. Welcome to the world of the Manhattan Distance:
http://en.wikipedia.org/wiki/Taxicab_geometry

wink

Not always I follow Euclid cheesy (its the cause of the diamond like structures..)
(hmm..tell me, have you used it in your latest formulaes?)

My mistake, I looked quickly and saw something else in the part where you take abs values, and then I tought you were diving by the magnitude, but it was a comment "//"  embarrass
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Aexion
Conqueror
*******
Posts: 116


The Fractal Hermit


WWW
« Reply #71 on: May 06, 2011, 06:50:32 PM »

The problem is that I don't know how to control bailout, so this must be done by Jesse sad

Oh, its not a bailout (well..you can use that as a bailout!).. I have changed the original mandelbox ballfold for a 4D hexadecachoron (I know..the name sounds weird..but thats the 4D version of the octahedron). If you change that, the arches and domes will dissapear, being replaced by a crystalline structure.
« Last Edit: May 06, 2011, 06:53:39 PM by Aexion » Logged

Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2512


Fragments of the fractal -like the tip of it


« Reply #72 on: May 06, 2011, 07:07:13 PM »

This is wild! grin Anyway, unable to modify Abox4D anyway, so we need the sacred holy power of Jesse! wink
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