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It is was not really easy; they need a folding (polyfolding is fine BUT with fix factor = 0), then a z rotation of 90°, then a Cayley transformation;

    z = ((z-i)/(z+i)) (on complex numbers)

And finally a x addition. Final result is on image. :D :D :D

Jesse I really need to do an example parameter, can I enclose it to the official binary? Thanks!!!

Sure, that's cool!

My regret is that polyfolding is discontinue. Fantastic patterns appear if you rotate but also weird cuts... Luckily Cayley Julia has not this problem - shows some mobius patterns using only continue funcs :)

I used the simplest method possible, z is simply linear scaled rather than mixed with mobius, probably there are a lot better
Still not understood how this can be done conformally in 3d... Will look again btw

When I finish testing will add ty... :)

Look like some futuristic Brazilian housing block.

 :D Thanks: I uploaded the updated files in the official downloads section! Also an amazingIfs example is available now... :dink: Enjoy!

(The example is more 3D looking due to a Z-add that makes the shapes fly away)

While trying to do a 3d version I found this... Apollonian volcanoes :o

Jesse I think that I can not do a "conformal" transform since it probably doesn't exist? :embarrass:

This parameter shows up almost perfectly with a raystep = 0.2 (0.5 is too much for my formula - do you think it's enuff? :angel1: )
Requires also Knighty's stars :dink:

Mandelbulb3Dv17{
V....Ej/..kB3...c....2....UcYYZLGJZ6.TU4Lad3o14EQ9dmyxAkqwPONIIGeBa2.33dsWIL4j.k
................................k182/uGTaz1........A./..................y.2.....
................/M.0/....6UV2...p0....E2.....U18dBDkojpD/.......aeKi0dkpXm1.H6T4
./EnAnYD12..0..........wz..................................u1....y1...sD...../..
.w1...sDVq2cNcUtjx1..........oIRMddbVcdjNSKYTzTqMunsZ2WRlVvIzMjfqOB5KtqDZ0yU4xu7
.uHxa6IqQMZPzOqdtFLQsCpD......ob3.............kD/2....sD..kz0...................
.............oAnAr1...sD....z.lRo4.grFP.EV5h/.DSo4.YtFP.kc5h/.hSo4......c....k1.
..................kz.wzzz1.U..6.P....M4...EB....W....k1....F....8/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc..k18XGQeGyD.sIRhrVAkz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................wSjE.Uyan9.D/0..0A.uPCj.wW9...U.cjt
w0UPwxSjE.Uyan9.cnrvx0/.uPCj.6LTjr92.cjtw0k.yxSjE.Uyan9.Furvx0/.uPCj.clTjr92.cjt
w0EczxSjE.Uyan9...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....A....E.....I....c....UMjVLG4B3......................................sU1....
/6.........aNaNaNaNiz.........zD........kz1........wz...........................
................................................................................
.....................2.....3....8....MqPgFqMpF5ChYYFH/..........................
.sU1..U......................UyD........3.2.......N/./..........................
................JJJJJJJJZzHJJJJJJJJtzIJJJJJJJJxj................................
................................/....E/...E0....//rPglqPnEI97NoI................
..............U/4MU.........................................UMzj................
........................6.2OaNaNaN4gz2QaNaNaNAyD................................
............................................}

Hi Darkbeam

Could not locate that formula - can you tell me where to find it?

see the first topic
28.0
Added a test version of Apollo 3D 

ERICR

 I tried it but I would like an example please
thank you all

DarkBeam you can flip every other polyfold backwards to remove the cut and get a kaleidoscope look.

@eiffie; not understood what you mean...

@cytotox: Knighty's "stars" refers to foldcut?-IFS shapes, I made them very recently... :D

@ericr: The param is an example param for Apollo3D, actually :D

A bit non-conformal should be ok, i think we are in pm on the way to improve it.
As you can see, the higher the iteration, the less accurate the DE becomes becuse the global scale parameter is not updated.
If z is also scaled, it should be ok even with 0.5 or higher multiplier (i hope)!

Nice examples of course, cool "Knighty" stars!  :)

from your parameter i only get  this  parallelepiped

did i miss something ?

yes because you do not have the new formulas installed
but be careful they are experimental

Do you refer to this http://www.fractalforums.com/index.php?topic=9810.msg27693#msg27693 or to this
http://www.fractalforums.com/mandelbulb-3d/mandelbulb3d-v1-7-7/?topicseen or to what else ?

(For the first 2 link i tough to have installed all but a couple of days ago now i see the content updated )

lately I do some confusion... but the home is the sticky thread :tease:

Yes, I get the same image, though I updated M3D as well as Darkbeams formulas yesterday (and again today). There must be something amiss still ...

don't know how to help

Anyway for jesse I get this, not good - as I was thinking. Because the formula is extremely sensible to small variations; the limit is a circle and you do not get here easily. :dink:

The only way to get a good result is my non uniform z scaling and afaik this is exactly Apophisis' approach for this fractal. Too bad...

Else you don't see the plane tiled correctly. The plane is filled on high iters, and if you scale x&y the limits are not reached. So... to get a visually appealing figure you must go non-conformal :dink:

 sorry but where is the formula apollo-3d corrected by jesse




ERICR

Not by Jesse by me. ;) ^ enclosed with that post's m3f ... more messed up than corrected ;D

Ok, got the test version - you can delete it for getting not in trouble with your version.

It seems not really to represent the latest suggestion, as it was.  And i guess the XY scaling is applied twice or so, and Z is affecting the filling too... very strange.

I guess we should do spend some more time into it because it really should work like the original version, only the Z scaling should be different.
If you don't like to, i would try to make it by myself (but could take some time).

I still don't understand Apollo3D. More 2D than 3D to me

EDIT/ OK, got the fixed one. Nice!

I can pass you the source code Jesse (have to write it for you)
Hi Jeremie :)

If you got the original formula in a higher language, that would be the best i think.
Then i can test it in pascal direct in the program, would be even more efficient than doing stuff over email and you had to write everytime another version.  :dink:

 :banginghead:  :drink:

I have an easy solution:
Just add a DE fix parameter at the end of the formula parameters and scale the global DE scale with this value, that should be about 1.2!
So you only need to add this somewhere in your apollo2d formula:
fld qword [esi+$70]
fmul qword [edi-$60] //where your DEfix parameter is
fstp qword [esi+$70]

The only change in shapes is about the DEstop value, because the DE is now calcuated better, the DEstop might be somewhere else.
Lower DEstop if this should be a prob.

Test without DEfix (upper image) and DEfix of 1.2 (lower image), both Raystep multiplier of 0.8:  :)

Yes Jesse, that will be great to do Apollo fractal without noise. I absolutely love them! Thank you and Darkbeam!

oh yeahhh!!!!

Do not know why I did not try this.

If I multiply z & the DE scale by the same value (the zmul... there is no need to introduce a defix because defix=zmul ;D :dink: )   it works for just any zmul! And with a perfect accuracy! You are a genius :ok:

Updated the official DL file :police:

Did you fix Apollo3D? Do you have an example param pliz?

No, do it seperate - not like Zmul.  Edit: Ok, like Abs(Zmul) should be ok!

And we should do update only the newformula zips, don't make everyone download the whole package again.
Only this time because the Apollo is already inside.  But in future...

Thanks!

Thank you again for everything but when all find time to sleep
Please may I have the param Vocan figure make in this  with topical Calyey
and called clayey
ERICR

It was a test fmla I deleted :embarrass: ... maybe I'll recover

I will fix some formulas currently buggy whenever possible, later

Couldnt resist to do some asm optimizations for the apollo2d, but because of the trig functions it is only ~15% faster...
Have attached it, if you like, take it or not.  :dink:

 ;D the trig functions essentially make this (see the crappy drawing)

1. find the quadrant of x,y
2. If the quadrant isn't the first, rotate x&y back to the 1st quadrant
3. if the quadrant is 2, 4, 6 ... then y = -y

Surely it's possible to optimize it at least for the case polyfold=3 (the classic gasket) but formula is less general :dink:

Also for a "true3D" version, we should try to check if x,y,z belongs to a "pyramid" over the origin, in this case rotate z-axis back to x-axis to make appear another branch in the z-axis. Else, do the normal formula + a lil rotation of xz (more or less) ;D (too complicated huh :sad1: ... I did not dare to try this!)

important; cayley transform flips x&y but it does NOT work - so before cayley I flipped them again (and maybe changed some signs)

param for ericr& friends


Mandelbulb3Dv17{
V.....S....O/...w....2....UbGNdVFhR9.XuZvv.21X2EtGT33QpgJzXiM6P.ha77.h2pCW0C56/k
................................sEUWPU/ZMz1........A./..................y.2.....
................/M.0/....6kr....f0....E2.....YpvK9RqqSsD...........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.w1...sDwUx2eDdm1yX1w/Lcq3QSzoeMMf/DJ4pDu8pgCLcblx9gdeQefh4RzYYBTU0k/CsDiznTzTmG
nxXx4PsVhWFUzq4Fcl13QerD......YP/.............kD.2....sD..kz....................
.............oAnAr1...sD....z.lRo4.grFP.EV5h/.DSo4.YtFP.kc5h/.hSo4......w....k1.
..................kz.wzzz1.U..6.P....M4...EB....W....k1....F....8/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc..k18XGQeGyD.sIRhrVAkz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR
S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq
40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................
E....6....E.....I....c....EEkx4PgxqA2pGG4B3..............................MU/46..
................................UJCoWgRyXz1.....................................
...0.BmqtvbOwGvDXcoS1y0HWzHCoWgRyydoz...........................................
.....................2.....3....8....6qPsZYFH/EPZZYFH/..........................
....Cs....E.0.................zD........kz1........wz.........zDsuFVf53iSy1.....
..............................................zD................................
................................}

 :beer:

thank you for the formula and thank you again for everything
you go too fast I have trouble keeping up in the last days

The only thing that comes in my mind (yet) is to limit the polyfold up to.. lets say 32, and have the cos and sin values stored in a lookup table.
Edit: The table would be to rotate the x,y values back to the first quadrant, but you need n-1 sin+cos values for each polyfold order, so a limit up to a order of 10 must be made...


The integer power rotation would stretch the metric, maybe there is some other math trick for polyfolding?


I know, i am an expert in spending many hours with similar tickling investigations without having any results  :dink:
(I let you do it, and if the result is ok i might do some asm optimization)  :dink:

No trick ... The fact is that polyfold is just a folding but based on regular quadrants instead of rectangular (infinite) slices. so it is strictly conformal in 2d, 3d, 4d... :)

hello, I have a book about measures of fractals and hyperbolic geometry (the circle of Apollonius)
did you think of the extent of Beiscovitch, a Lebesgue measure (made ​​for fractals)
distance poincare used geometreie hyperbolic
J hope to help
ERICR

That is the theory, but for a real formula you must take into account not only one complex transform (like the theory says) but a minimum of 3 (possibly forming a sym pattern, for keeping things simple - even if in general you know, an Apollonian gasket can be made of N circles of different radius. Images; http://en.wikipedia.org/wiki/Apollonian_gasket#Integral_Apollonian_circle_packings  ;D .But it was already hard to make the basic version!...  :o :-\ ). Remind that you must stick to non-probabilistic methods! So blabla... In the end the only way to get there in MB3D is to use a polyfold (kaleidoscope) transform and after it a Mobius one. :)