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Author Topic: New numbers set.  (Read 5547 times)
Description: Perhaps this new number is interesting for the generation of fractals in 3D
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FFDiaz
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« Reply #15 on: December 31, 2011, 02:04:24 AM »

Let's suppose that we begin for the case in which the coefficient of h is zero, that is to say, the coordinate x of every point of the studied space it will be positive. So :
c=cxo*g+cy*i+cz*j
I think that it is clear that the points that we have to study belong to a three-dimensional space.

We shall define the following variables:
     cxo  //x coordinate of each point in R^3
     cy   //y coordinate of each point in R^3
     cz   //z coordinate of each point in R^3

     txo  //xo coefficient of number t belonging to RC3 (t=xo*g+x1*h+y*g+z*j)
     tx1  //x1 coefficient of number t belonging to RC3
     ty   // y  coefficient of number t belonging to RC3
     tz   // z  coefficient of number t belonging to RC3

and to calculate the iteration function f(t)=t^2+c
     txo=txo*txo+tx1*tx1+cxo
     tx1=2*txo*tx1+ty*ty
     ty=2*ty*(txo - tx1)+tz*tz+cy
     tz=2*tz*(txo-tx1+ty)+cz

to find out if diverges the iterative process we check if

     (txo-tx1)^2+ty^2+tz^2< a
    
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DarkBeam
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« Reply #16 on: December 31, 2011, 10:50:02 AM »

Let's suppose that we begin for the case in which the coefficient of h is zero, that is to say, the coordinate x of every point of the studied space it will be positive. So :
c=cxo*g+cy*i+cz*j
I think that it is clear that the points that we have to study belong to a three-dimensional space.

We shall define the following variables:
     cxo  //x coordinate of each point in R^3
     cy   //y coordinate of each point in R^3
     cz   //z coordinate of each point in R^3

     txo  //xo coefficient of number t belonging to RC3 (t=xo*g+x1*h+y*g+z*j)
     tx1  //x1 coefficient of number t belonging to RC3
     ty   // y  coefficient of number t belonging to RC3
     tz   // z  coefficient of number t belonging to RC3

and to calculate the iteration function f(t)=t^2+c
     txo=txo*txo+tx1*tx1+cxo
     tx1=2*txo*tx1+ty*ty
     ty=2*ty*(txo - tx1)+tz*tz+cy
     tz=2*tz*(txo-tx1+ty)+cz

to find out if diverges the iterative process we check if

     (txo-tx1)^2+ty^2+tz^2< a
    

Mumble, I can implement a version of this in MB3D using w coordinate instead of  tx1, but MB3D checks divergence in the standard way only;

x^2+y^2+z^2+w^2< a

and not

(x-w)^2+y^2+z^2< a

the difference is; -2*w*x  undecided anyway... I try to implement it in MMFwip3d at first to see the correct effect. smiley If I am able to understand correctly everything that is  police
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weavers
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« Reply #17 on: December 31, 2011, 12:44:41 PM »


Must, Trust, in the force Darkbeam! Do it before the year of the 12!
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David Makin
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« Reply #18 on: December 31, 2011, 04:40:52 PM »


<snip>
the difference is; -2*w*x  undecided anyway... I try to implement it in MMFwip3d at first to see the correct effect. smiley If I am able to understand correctly everything that is  police

Actually even I don't use that usually when testing an idea quickly - I normally use a copy of Ron Barnett's "3D Fractal Raytrace" formula from reb.ufm and simply replace either the QuatJulia or QuatMandelbrot sections with the test code (with DE parameter set to Vepstas) - in this case it'll be much easier to adjust any magnitude calculations in that than in my wip formula wink
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #19 on: December 31, 2011, 05:03:41 PM »

Hey you! I just implemented your Makin mandelbrot sets 1,2,3,4! wink

The new number set is harder to do I think Azn Happy new year dancing banana dancing banana dancing banana


* gedatou.jpg (61.5 KB, 795x563 - viewed 352 times.)
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David Makin
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« Reply #20 on: December 31, 2011, 10:06:47 PM »

Hey you! I just implemented your Makin mandelbrot sets 1,2,3,4! wink

Yey ! Though I much prefer the non-standard Mandelbulb types - "Sim.Rot. ZX" etc. - I'm sure some of which haven't been transferred to other 3D software yet.

I really must get around to documenting that formula and releasing it properly as a non-WIP one to the formula database !!
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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #21 on: December 31, 2011, 10:55:19 PM »

I have seen! Some formulas are kimda weird or similar to standard ones some others look good. Maybe I will implement some (what are the best ones?). And there is also Mandelview available in Mandelbulb3d ... found in a forgotten place cheesy
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David Makin
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« Reply #22 on: January 01, 2012, 06:07:11 PM »

I have seen! Some formulas are kimda weird or similar to standard ones some others look good. Maybe I will implement some (what are the best ones?). And there is also Mandelview available in Mandelbulb3d ... found in a forgotten place cheesy

The best thing I can do there is probably let you make up your own mind:

Rucker:
http://makinmagic.deviantart.com/art/Out-on-the-Rim-142136488   (old version of code, renders better now)
http://makinmagic.deviantart.com/art/Sporocarp-quot-fruiting-body-quot-142383128

Thornton 2:
http://makinmagic.deviantart.com/art/Woodfest-142210135
http://makinmagic.deviantart.com/art/Woodhome-143575363

Sim. Rot. XYZ (Simultaneous Rotation in 3 angles)
http://makinmagic.deviantart.com/art/Hairy-Ball-144652915

Sim.Rot. ZX
http://makinmagic.deviantart.com/art/Terraformed-Mars-144722355

Norm.Sim.Rot. XYZ (Norm.==normalised)
http://makinmagic.deviantart.com/art/A-Martian-Delicacy-144901891
http://makinmagic.deviantart.com/art/Under-Red-Skies-145191644
http://makinmagic.deviantart.com/art/Centauri-Prime-145239769

"Nylander" (from an old formula version - a suggestion by Paul Nylander that I tried and can be interesting)
My implementation here:
Code:
           magn = (z1=sqrt(magn))^@mpwr
            r = |zri|
            if r==0.0
              zri = cri
              zj = cj
            else
              ph = @mpwr*asin(zj/z1)
              th = @mpwr*atan2(zri)
              x1 = (sqr(real(zri))*cos(ph)+sqr(imag(zri)))/r
              y1 = real(zri)*imag(zri)*(cos(ph)-1.0)/r
              zj = -magn*real(zri)*sin(ph)/sqrt(r)+cj
              zri = magn*(x1*cos(th)-y1*sin(th)+flip(x1*sin(th)+y1*cos(th)))+cri
It produced: http://makinmagic.deviantart.com/art/Theme-Park-Ride-146314193

Cons.Rot. ZX (consequetive rotations about 2 axes)..
http://makinmagic.deviantart.com/art/The-Lost-Isle-145246194

Also there are more from about here:

http://makinmagic.deviantart.com/gallery/?offset=24

In particular Alien Archeology, On the reef  (Norm.Sim.Rot.ZX), Limestone Pavement, Shropshire Crags, (Norm.Sim.Rot.XYZ), Assorted Toffee Wrappers (Sim 3D angles), Summer on the Tundra (Sim.Rot.ZX), Temple of the Anointed (Cons.Rot.ZXY)
« Last Edit: January 01, 2012, 06:36:18 PM by David Makin » Logged

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DarkBeam
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Fragments of the fractal -like the tip of it


« Reply #23 on: January 01, 2012, 06:38:04 PM »

Well, I arrived at this conclusion;

I would exclude the formulas that give strong "whipped cream" effects, strange stuff in general, or with visual outcome nearly identical to existing ones. smiley

Thornton formulas are really similar to existing ones, except for thornton2 that is interesting but imo has a strange look. (In fact it uses strange angles...) wink

"cons.rot." fmlas can be obtained with my "General" formula, probably? (It handles all formulas obtainable with two angles)

Norm.Sim.Rot. XYZ; I like a lot the visual result of this one so I included it! A Beer Cup

Sim.Rot. XYZ - It makes less sense ... and in fact "not Normalized" formulas always look less interesting than the "corrected ones" cheesy

"Nylander" ... i don't know how it looks, the detail you chosen shows strong deformations... smiley

Sorry but I can't include just everything wink time constraints and so on smiley
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FFDiaz
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« Reply #24 on: January 01, 2012, 10:50:32 PM »

I am annihilated before so much deployment of technical resources. I have the sensation of having woken up the attention of the big gurus of Mandelbrotland.

Again, thank you very much for the effort that you are doing for giving form to my ideas.

 Happy 2012 to all.
 Paco Fdez.
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DarkBeam
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« Reply #25 on: January 01, 2012, 11:26:15 PM »

David is a guru for sure, I am a kiddy wink

Sorry for the hijackment, wait wait... One day I will reach that brot wink
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David Makin
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« Reply #26 on: January 02, 2012, 12:24:10 AM »

I am annihilated before so much deployment of technical resources. I have the sensation of having woken up the attention of the big gurus of Mandelbrotland.

Again, thank you very much for the effort that you are doing for giving form to my ideas.

 Happy 2012 to all.
 Paco Fdez.

Apologies from me too for going OT in your thread - I must remember that it's possible to use messaging as well as threads wink

At *some* point I will get back to both my Wip3D formula for UF (and try implementing your new numbers and similar ideas) *and* to my semi-updated 3D IFS formula which is halfway updating to being able to render primitives in a similar way to Jesse's dIFS but handles any (affine) IFS "correctly".
Then on to a full 3D IFS tree formula that uses DE instead of Hart's method so that any non-linear divergent transforms can be used as well as affine ones.
And then......I may be dead !
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David Makin
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« Reply #27 on: January 02, 2012, 12:27:44 AM »

<snip>
I would exclude the formulas that give strong "whipped cream" effects, strange stuff in general, or with visual outcome nearly identical to existing ones. smiley


smiley Tempting idea - but some whipped cream can look really good - for instance "Theme Park Ride" (from Paul Nylander's suggestion) is all about whipped cream, but I think it's still a great image - plus of course once converted to glass objects in Bryce or whatever even some Julia quaternions look pretty cool smiley
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http://www.fractalgallery.co.uk/
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Kali
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« Reply #28 on: January 11, 2012, 02:42:29 AM »


Must, Trust, in the force Darkbeam! Do it before the year of the 12!

Yeah... Luca, the force you must use. Do Paco's brot and my mandelbox surface suggestion for tomorrow, or to Yoda I will tell you are lazy Fractal Jedi.

 grin grin grin
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FFDiaz
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« Reply #29 on: January 24, 2012, 12:52:13 AM »

Luca,I have a doubt, when you calculated the attached image now you used (tx0-tx1)^2+ty^2+tz^2 for to find the end of iteration?

Thanks.
Paco


* gedatou.jpg (61.5 KB, 795x563 - viewed 337 times.)
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