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 threedimensional 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*(txotx1+ty)+cz to find out if diverges the iterative process we check if (txotx1)^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 threedimensional 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*(txotx1+ty)+cz to find out if diverges the iterative process we check if (txotx1)^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 (xw)^2+y^2+z^2< a the difference is; 2*w*x anyway... I try to implement it in MMFwip3d at first to see the correct effect. If I am able to understand correctly everything that is



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weavers


« 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


« Reply #18 on: December 31, 2011, 04:40:52 PM » 

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



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




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David Makin


« Reply #20 on: December 31, 2011, 10:06:47 PM » 

Hey you! I just implemented your Makin mandelbrot sets 1,2,3,4! Yey ! Though I much prefer the nonstandard 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 nonWIP one to the formula database !!



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DarkBeam
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« 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



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David Makin


« 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 The best thing I can do there is probably let you make up your own mind: Rucker: http://makinmagic.deviantart.com/art/OutontheRim142136488 (old version of code, renders better now) http://makinmagic.deviantart.com/art/Sporocarpquotfruitingbodyquot142383128Thornton 2: http://makinmagic.deviantart.com/art/Woodfest142210135http://makinmagic.deviantart.com/art/Woodhome143575363Sim. Rot. XYZ (Simultaneous Rotation in 3 angles) http://makinmagic.deviantart.com/art/HairyBall144652915Sim.Rot. ZX http://makinmagic.deviantart.com/art/TerraformedMars144722355Norm.Sim.Rot. XYZ (Norm.==normalised) http://makinmagic.deviantart.com/art/AMartianDelicacy144901891http://makinmagic.deviantart.com/art/UnderRedSkies145191644http://makinmagic.deviantart.com/art/CentauriPrime145239769"Nylander" (from an old formula version  a suggestion by Paul Nylander that I tried and can be interesting) My implementation here: 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/ThemeParkRide146314193Cons.Rot. ZX (consequetive rotations about 2 axes).. http://makinmagic.deviantart.com/art/TheLostIsle145246194Also there are more from about here: http://makinmagic.deviantart.com/gallery/?offset=24In 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 »

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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. 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...) "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! Sim.Rot. XYZ  It makes less sense ... and in fact "not Normalized" formulas always look less interesting than the "corrected ones" "Nylander" ... i don't know how it looks, the detail you chosen shows strong deformations... Sorry but I can't include just everything time constraints and so on



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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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Fragments of the fractal like the tip of it


« Reply #25 on: January 01, 2012, 11:26:15 PM » 

David is a guru for sure, I am a kiddy Sorry for the hijackment, wait wait... One day I will reach that brot



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David Makin


« 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 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 semiupdated 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 nonlinear divergent transforms can be used as well as affine ones. And then......I may be dead !



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David Makin


« 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. 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



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FFDiaz
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Posts: 18


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

Luca,I have a doubt, when you calculated the attached image now you used (tx0tx1)^2+ty^2+tz^2 for to find the end of iteration?
Thanks. Paco



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