Logo by Trifox - Contribute your own Logo!
News: Visit the official fractalforums.com Youtube Channel
 
*
Welcome, Guest. Please login or register. July 21, 2017, 02:40:05 PM


Login with username, password and session length



Pages: 1 ... 3 4 [5]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Quadray Sets  (Read 11587 times)
Description: Quadray representations of the mandelbrot set
0 Members and 1 Guest are viewing this topic.
Aexion
Conqueror
*******
Posts: 116


The Fractal Hermit


WWW
« 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;

}
 
Logged

Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2506


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

No sweat, guardian of wisdom!
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2506


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 363 times.)
Logged

No sweat, guardian of wisdom!
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2506


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.....
................................................................................
................................}
Logged

No sweat, guardian of wisdom!
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
Logged

Fractals all the way..
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)

Logged

|</\|_|
░░░░░░░

http://fractkali.deviantart.com/
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?)
Logged

Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2506


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
Logged

No sweat, guardian of wisdom!
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.. :)
Logged

Fractals all the way..
Incendia for 3D Fractals
Aural for Musical Fractals
DarkBeam
Global Moderator
Fractal Senior
******
Posts: 2506


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
Logged

No sweat, guardian of wisdom!
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
Logged

|</\|_|
░░░░░░░

http://fractkali.deviantart.com/
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: 2506


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
Logged

No sweat, guardian of wisdom!
Pages: 1 ... 3 4 [5]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
Virtual investigation to Mandelbrot sets and Julia sets Mandelbrot & Julia Set Jules Ruis 0 1835 Last post October 19, 2006, 06:36:54 PM
by Jules Ruis
Transformations Between Self-Referential Sets General Discussion Nahee_Enterprises 0 824 Last post April 18, 2009, 02:50:18 AM
by Nahee_Enterprises
3D Julia sets 3D Fractal Generation kronikel 0 1524 Last post August 06, 2011, 10:35:30 PM
by kronikel
My first 3d render sets! Images Showcase (Rate My Fractal) skyk 3 449 Last post December 07, 2012, 01:33:24 PM
by cKleinhuis
Hausdorff of hypecomplex J-M sets (new) Theories & Research snayperx 2 234 Last post March 30, 2014, 04:38:19 PM
by Endemyon

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 0.174 seconds with 29 queries. (Pretty URLs adds 0.015s, 2q)