Apollonian fractals

[DarkBeam]

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.

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

[Jesse]

Sure, that's cool!

[DarkBeam]

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...

[matsoljare]

Look like some futuristic Brazilian housing block.

[DarkBeam]

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

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

[DarkBeam]

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

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

[DarkBeam]

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? )
Requires also Knighty's stars

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................................
............................................}

[cytotox]

...
Requires also Knighty's stars
...

Hi Darkbeam

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

[ericr]

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

[eiffie]

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

[DarkBeam]

@eiffie; not understood what you mean...

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

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

[Jesse]

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

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

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! 

[PhotoComix]

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? )
Requires also Knighty's stars

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................................
............................................}

from your parameter i only get  this  parallelepiped

did i miss something ?

[DarkBeam]

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

[PhotoComix]

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 )