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Author Topic: An old formula revised  (Read 25737 times)
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hgjf2
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« Reply #90 on: October 25, 2012, 07:05:21 PM »

Ask:  how to winning the prises for the FRACTALFORUMS competitions? The prises come via post or on card?
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Alef
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« Reply #91 on: October 28, 2012, 07:20:00 PM »

Ask:  how to winning the prises for the FRACTALFORUMS competitions? The prises come via post or on card?

hurt What competitions? Why do you ask here and not dedicated pages. And what you expect from enthusiast based community What The F@ck ??
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hgjf2
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« Reply #92 on: October 29, 2012, 08:55:18 AM »

hurt What competitions? Why do you ask here and not dedicated pages. And what you expect from enthusiast based community What The F@ck ??
I believed and knew that the chapter "The 3D Mandelbulb" being a special fractal competition because have the subchapters "Let's put theory", "Let's put videos", "Let's put mplementations" , "Rendering" same as the chapter "Competitions and contents". And I knew this that current month it posting at some topic
"Old formula revised" exacthly in MAY when working at the annual fractal competitions, and I knew this the chapter have same organisation mode as the chapter "Competition and contents" and this chapter have certain texts and images copied from topic "Competition and contents".
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Alef
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« Reply #93 on: October 30, 2012, 04:00:39 PM »

If you meant this:
http://www.fractalforums.com/index.php?action=gallery;cat=3

Then you should go here with winers recieving calendars:
http://www.fractalforums.com/5th-annual-fractal-art-competition-2012/competition-2012-and-the-winners-are/

Quest for finding real 3D mandelbrot aka Holy Grail set is something other. If someone would find it, he would have dedicated article in wikipedia and his name eternalised in history of science;)
« Last Edit: October 30, 2012, 04:05:54 PM by Asdam » Logged

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Alef
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« Reply #94 on: November 06, 2012, 07:16:18 PM »

Almoust the same spot, but more colours:


Code:
Clock_of_Branches_2  {
  credits="Asdam1;10/3/2012/20/17"  commentTemplate="Saved on $month$\
  , $day$ $year$ at $hour$:$min$:$sec$\nDate: $date$\nTime: $time$\nR\
  esolution: $xdots$ x $ydots$\nCalculation time: $calctime$\nVersion\
  : $version$"
  CommentText="Saved on Nov, 4 2012 at 01:44:10\nDate: Nov 4, 2012\nT\
  ime: 01:44:10\nResolution: 480 x 360\nCalculation time: 00:02:07.11\
  8\nVersion: 4.0"
  creationTime=2012/10/3/20/17/28 saveTime=2012/11/4/1/44/10
  Creator="Asdam1" ModifiedBy="Asdam1" calcTime=127118 version=4.0
  Type=Quaternion Subtype=0 Width=480 Height=360 DisplayDepth=24
  gamma=+1.1 roughness=+0.03 AOIntensity=+0.4 DOFEnabled=+1
  DOFAperture=+0.125 DOFFocalLength=+0.0692849163391902
  DOFPlaneDistance=+0.13856983267838 FogEnabled=+1 FogRed=23
  FogGreen=21 FogBlue=137 FogFront=+0.0610336979595676
  FogBack=+0.35890555522641 FogDensity=+3.07612387515116
  FogLinear=+0.05 FogSquare=+0.05 FogExp=+0.2
formula:
  filename="Mag xyz forms.cfm" entry="cp_85362" p_bailout=77700000000
  p_inversebailout=0 p_fractaltype="Mag Mandy 2 fast"
  p_colortime="Post Mandy Post Rotation" p_pixelmode="+ no abs"
  p_symmetrymode="YZ Switch     very nice" p_seed=-0.5 p_juliaMode=0
  p_Detail_Switch=1 p_bmode="Pi/2" p_checkvarset=2 p_amode="b^(3-n)"
  p_checkvarsetA=0.1 p_radswitch=0 p_n=2 p_pixeln=2 p_c=0/0/0/0
  p_addyzpixel=0 p_spokes=3 maxiter=7 highresmult=10 backtrace=10
inside:
  filename="NumberSeekerColouring.ccl" entry="LogTrichrome"
  p_pallete="Fractal Explorer like" p_posneg=0/0
  p_lgtype="1- Triple logarithm" p_darkness=3 p_postfn="1- None"
  p_switchRB=0 p_baseR=1.35 p_baseG=1.55 p_baseB=1.65 solid=0
  background=0
dimensional:
  observer=0.09852919331003/-0.039523053619068/-1.0256463577236
  topview=-0.051677551569366/0.94569859380349/-0.32091057997811
  viewpoint=-0.49607723609472/0.98369642435929/2.0854540178502
  backClippingPlane=3.3285493523157 viewangle=36
lighting:
  lightModel=0 light0Shadow=yes light1Enabled=yes light1Shadow=yes
  light4Enabled=yes light4Shadow=yes
gradient:
  smooth=yes colormodel=CM_RGB knotmode=all dragknotmode=global
  Offset=0 knotrgb=(0,255,248,231) knotrgb=(43,128,0,64)
  knotrgb=(85,255,248,231) knotrgb=(127,255,120,70)
  knotrgb=(170,34,33,25) knotrgb=(214,165,217,0)
}
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M Benesi
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« Reply #95 on: November 07, 2012, 02:55:10 AM »

  Candyland.  cheesy

   I've noticed that this particular fractal type allows a lot of mathematical manipulations, and maintains fractally goodness, a lot like the 2d Mandelbrot. 

  Eventually I'll get around to posting some of the various things one can do.  For now, we are still waiting on an implementation by Luca (DarkBeam).    Luca- if you notice this, you might want to implement this formula in a totally different way.  I'll put up some code eventually- it will be a LOT simpler than the original code I posted for you. 

  I've also figured out, or in all likelihood rediscovered, a few more "transforms" that can be applied to a majority of (2d and 3d) fractals. 
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Alef
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« Reply #96 on: November 08, 2012, 03:39:21 PM »

You 'll be more sucsessfull with syntopia. Darkbeam and Jesse for some time had halted programming  A Beer Cup
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M Benesi
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« Reply #97 on: November 09, 2012, 03:43:42 AM »

  Cool.  I understand the need for a break now and then. 

  I've been thinking about fragmentarium for a bit... just taking a break for a while.   
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M Benesi
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« Reply #98 on: November 17, 2012, 09:53:52 AM »

Fragmentarium code is over in the "non-de" thread.  I'll copy it over here when I iron it out.  For now, check out the gears grinding away.  I'll update ChaosPro code with this (rotation type) option in a bit:

<a href="http://www.youtube.com/v/Ih4k5KZAVxg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Ih4k5KZAVxg&rel=1&fs=1&hd=1</a>

  Here is the new very interesting hollow z^2 Mandy type, based on this same formula.

<a href="http://www.youtube.com/v/Au8iBwCbaIE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Au8iBwCbaIE&rel=1&fs=1&hd=1</a>
« Last Edit: March 16, 2013, 05:28:14 AM by M Benesi » Logged

M Benesi
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« Reply #99 on: March 16, 2013, 05:41:05 AM »

  Ok.  I never updated the ChaosPro code to add in the above variant (hollow one above this post- second youtube clip). 

  After rotating the x axis to the vector (-1,-1,-1) to (1,1,1), don't use the mag xyz formula.

  Use :
Code:
nx= 2*(abs(sx) + seed);   //  with seed around -.5   
ny= 2* (abs(sy)+seed);
nz=2* (abs(sz)+seed);
  Now rotate back from the vector axis to the x axis. 

  You can combine the result of this with the mag xyz- just calculate each separately and vary the weight of each part as you wish.

  Anyways, it's a nice little trick you can do with any of the rotation based fractals.  I implemented this in the fragementarium code for this fractal (in the "non-de" thread), although I haven't gotten around to creating a coloring method that allows the bling of ChaosPro palette mode for fragmentarium. 
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laser blaster
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« Reply #100 on: April 13, 2013, 10:56:24 PM »

Wow, that's fantastic! grin I don't know if it's the holy grail, but it sure looks like it.I'd love to see some pictures of the full XYZ Mandy version, even if it's a chaotic mess.

I'm trying to understand the math behind what you did here. Looking at the code on page 4, in the initialization code, it looks like you first rotate the coordinates such that the former x-axis aligns with the axis (1,1,1). Then you initialize two variables A and B. Moving on to the iteration part, it looks like you convert the coords to polar form, multiply the angles by pixeln(which I assume is just the chosen power, i.e. 2), convert back to standard form, and add a seed to the X,Y,Z values.

But there are some things I don't understand. It looks like you do more than the typical "multiply the angles by n and raise the length to power n". What do r1, r2, and r3 do? And what role do the a and b variables play? The math of it is all right there on the page, but I don't have a full grasp of what it actually does, in geometric terms.

Then the rest seems easy enough to understand. First you de-rotate everything back towards the x-axis. Then you add in the initial (unrotated) x pixel component. Then you do the detail switch, and rotate the whole thing once again.

It would be awesome if you could clear up my points of confusion, and any misconceptions I have about the formula. Thank you for your time.
« Last Edit: April 13, 2013, 10:59:55 PM by laser blaster » Logged
M Benesi
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« Reply #101 on: April 29, 2013, 07:43:09 AM »

  I've been in the middle of moving my parents, and now I have a lot of stuff to take care of at their new place.  I've a bunch of stuff to take care of over the next week or so, but hopefully will have a bit of free time to explain things.

  Basically, there is a 45 degree rotation, followed by a (90-54....) degree rotation (90-magic angle).  This rotates to the 1,1,1 axis; then one later *** rotates back to the x-axis by reversing the process (or maybe I have it backwards- relatively buzzed right now, and definitely not in the mood to check my math). 

  ***  Rotate back to the other axis after applying the transform, which can be any transform one desires, as long as it works.  Which isn't saying much. 

  For example:

  take all 3 coordinates absolute value and subtract 1 (or something else) from them, assigning the new values to the corresponding coordinate ******, then rotate back. 


******  such as x=  abs (x) - 1;     y = abs (y) -1; .....


  Anyways, pretty awesome what one can get with this simple trick.  Too bad I've been pulling oranges out of the apple bin for a while.  Or maybe not.  I hate apples.
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jehovajah
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« Reply #102 on: May 02, 2013, 03:50:29 AM »

Fragmentarium code is over in the "non-de" thread.  I'll copy it over here when I iron it out.  For now, check out the gears grinding away.  I'll update ChaosPro code with this (rotation type) option in a bit:

<a href="http://www.youtube.com/v/Ih4k5KZAVxg&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Ih4k5KZAVxg&rel=1&fs=1&hd=1</a>

  Here is the new very interesting hollow z^2 Mandy type, based on this same formula.

<a href="http://www.youtube.com/v/Au8iBwCbaIE&rel=1&fs=1&hd=1" target="_blank">http://www.youtube.com/v/Au8iBwCbaIE&rel=1&fs=1&hd=1</a>
Wow! Matt. Way cool!

And the gears rotate the right way too!
I am going to need this type of functionality in my fluid dynamic analysis thread at some stage soon .
The rotations preserve the regional boundaries but I want to model fluid flows that persist vortices even as the boundary constituents flow into each other.

The holy grail is an inspiring goal, but dude this is way cooler than that!
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
M Benesi
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« Reply #103 on: May 04, 2013, 08:06:46 AM »

  Drunk post.  cheesy     
« Last Edit: May 25, 2013, 06:48:34 AM by M Benesi » Logged

M Benesi
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« Reply #104 on: May 25, 2013, 07:32:18 AM »

All right.  I made a pretty big error in the math of this formula, although it still turned out pretty nice looking.  Update: on second thought, checked the math, it was correct before.  The version below has the pi/4 rotations, but one should use the pi/2-magic angle versions.  

   Here is a much simpler version to play with (no Mag xyz portion of the formula).

  You can switch the order of the formula, putting the Mandelbulb portion first, then the rotation to the ABS portion, followed by the ABS portion, then the rotation back to the Mandelbulb portion.  If you do switch the order, you probably want to make the new z component (at the bottom of the Mandelbulb portion) negative.  "Trust me, I know what I'm doing."  A great quote...      anyways, switching the order makes it more Mandelbrot shaped.  

sx= part x of pixel
sy= part y of pixel
sz= part z of pixel

whiskey= sqrt(1/2);

Code:
// rotate to absolute value axis

//rotation around y axis

nx= sx  * whiskey -  sz * whiskey;
sz= sx  * whiskey +  sz * whiskey;
sx=nx;

//rotation around z axis

nx=sx * whiskey - sy * whiskey;
sy=sx * whiskey + sy * whiskey;
sx=nx;

// ABS portion of the formula

sx= 2* abs(sx) - 1;     // you can use different values besides 1,  it's a good arbitrary
sy= 2* abs(sy) - 1;    // starting value... use the same value for all 3 variables!@!!
sz= 2* abs(sz) - 1;    //  bloop

// rotate back to Mandelbulb x-axis

//rotation around z axis

nx= sx* whiskey + sy*whiskey;
sy=-sx* whiskey + sy*whiskey;
sx=nx;

//rotation around y axis

nx= sx  * whiskey +  sz * whiskey;
sz=-sx  * whiskey +  sz * whiskey;
sx=nx;

// Here is the Mandelbulb part

r2=(sqr(sx)+sqr(sy)+sqr(sz))^abs(n/2);  //magnitude

r1=sqrt(sqr(sy)+sqr(sz));   // for the angle

theta=atan2((sx)+flip(r1))*n;
phi=atan2((sy)+flip((sz)))*n;

nx=r2*cos(theta);
nz=(r2*cos(phi)*sin (theta));     // new z and new y are switched to
ny=(r2*sin(phi)*sin (theta));   // make it more symmetric- I like it a bit more  

if (Julia) {
sx=nx + x_component;
sy=ny + y_component;
sz=nz + z_component;
} else {
if (x_pixel<0) {
sx=nx + x_pixel_component;    // whole component below zero
} else {
sx=nx+ .5* x_pixel_component;  //  .5 * component above zero
}

sy=ny;   // no pixel components for these guys!!!
sz=nz;
}

// now check bailout, repeat iteration




  Here is some interesting math for you:
Code:
r1=1/sqrt(3);
r2=(1-r1)*.5;
nx=(sx+sy+sz)*r1;
ny=r2*(sy-sz)+(sy-sx)*r1;
sz=r2*(-sy+sz)+(sz-sx)*r1;
sx=nx;
sy=ny;

//rotation around x axis

ny= -sy  * sqrt(1/2) + sz * sqrt(1/2);
sz= +sy  * sqrt(1/2) + sz * sqrt(1/2);
sy=ny;

// is more or less the same as:

//rotation around z axis

nx=sx * sqrt(1/2) + sy * sqrt(1/2);
sy=-sx * sqrt(1/2) + sy * sqrt(1/2);
sx=nx;

//rotation around y axis

nx= sx  * sqrt(2/3) +  sz * sqrt(1/3);
sz= -sx  * sqrt(1/3) +  sz * sqrt(2/3);
sx=nx;



//  (as long as I did the correct rotation directions)


  What is the difference between the 2?  cheesy  
« Last Edit: May 26, 2013, 07:49:33 AM by M Benesi » Logged

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