Apollonian Gasket 3d

[jotero]

Hello all  

Fractal Octagon folding + Sierpinski "hyperbolic 3D"



 
http://www.evolution-of-genius.de/kleinian_groups_hyperbolic_sierpinski_b.png

Code:

Mandelbulb3Dv18{
g.....s/...U5...ET...2A...Ep95r/...6.rblFwzzzr3ER9MTb8B9WxnVFDEeGnWMzo23rEmhjM1E
................................nAnAnAnA1z1........Y./.........E........y.2...wD
...Uz6/...Ud1.../M.1/......K2...kK....E0.....IzP28XSPtrD/.kNVxsD...m/dkpXm1.OaN4
z.....cD12..12.........zz0......czyD........wz9...........U0.....y1...sD...../..
.wXaNadD/H6yjcrKCy1..........WzQciCNSXfjI58ZWapLYrPk2Wz9uhZXz.fNGaCNSXfjlOaYdHar
suXynVuuYtBiykMagpWSPtsDU.....I/A/.............E.6....sD..G.....................
.............oAnAt1...sD....zw1...................................kNVxsDO0....x/
.....Ksulz1.......kz9wzzzH.U..6.U....o1...EB....V.9X5U3.UT.F....8/...Yn1...UJl5A
...U.ydelyjeYFnzTeOgzf8No.6618nzE07Y...KXAYl5IyD6UA8EVQ2wz9..0........k.C.kXWF1.
................................/6U0.wzzz1...........M1........./.........E.0c..
zzzz............n/...................2W.8.kzzzD..YZyCPZaLz98ETj/1hz..1..........
/6U0.wzzz1...................................srbF/EIOVJHzzlHMm7.L75PctzDbdsb.UAm
4jLzT7LWP/kF93oFQsrhGG5.EaeZB/bTqN5Q.62AVo2lyteeX0kHlkIHMwrc4V6.XHysBlqTNd7M.o4E
6p2kzB8iW/Eb/pMH..kfvCIJzzFEtKMdyzHQXZudxz3cpGsU................................
E....MEJF3E.....I....c....kHXFLM4J5PgZYFH/EM.A3..E4.......................U/4MU/
4M........UmAnAnAnAjz.........zD................................................
................................................................................
.....................A/....3....1....wZIjFLMoJ4.................................
4MU/.........................50E........N.2........2./..........................
................................................................................
.....................................wzzzzD......MoPgFKOiRKGXxqQV/kR............
..........U/4M...MU/4MU/................................................kz1.....
.......................U4/2.....................................................
................................................zzzzz1......4x4PYZaPbFJNo7LMnE4.
.....................6U.C...4MU/4M.................wz.........zD................
................................................................................
......................................................6....3....3....2YEjVLHjFqG
VlKO.65..........................QU1..........................zj..........kAnAnA
nAnuz.........zDnAnAnAnAfz1.....................................................
................................................................/....E/...U0....
HZKNm/LOiBrOdB1.m/..............................4MU/4MU/........nAnAnAnAvz1.....
...wz.........zD........kz1.............................cz1.....................
............................................................................}
{Titel: jotero 2015}

ciao
torolf

[ericr]

 sublime as always, but we could do that mathematically with the transformation of mobius, inversions  and groups see the indications of JOS LEYS
I try but it is very difficult


ERICR

Fractal  realized wich your method

[Chillheimer]

thank you for sharing the formulas and parameters! really a lovely fractal style!

I played around with your last parameters (Fractal Octagon folding + Sierpinski "hyperbolic 3D) and this came out:

Fullview: http://nocache-nocookies.digitalgott.com/gallery/18/7776_16_07_15_11_20_09.jpeg
parameters:

Code:

Mandelbulb3Dv18{
g......3...E9...ET...2A...kV68BFHFV0.bSkmIw0oe2E9ogao/gO8.Yzziw7jic4.Lda38PyQU.k
................................zbSn4W8th.2........Y./.........E........y.2...wD
...Uz6/...UZ/.../M/1/.....k96...hK....E0......s3QUVFzojD/.k8q5QE...6/xa21i1.OaN4
z.....cD12..12.........zz0......czyD........wz9...........U0.....y1...sD...../..
.wXaNadD.ZGbrWaaawH/jpz7LLY6zIKGplS89cjjCanBUR48Ww90R.ne4I97zgCbPdS6kClj8fqzkepk
yvvLrLRRx5o2zAw//xvzMhmDU.....IaB/.............E.6....sD..G.....................
.............oAnAt1...sD....zw1...................................Ezb1dER0....x/
.....Ksulz1.......kz.sTgl0.4.63.4/...g3...UE....8....k1...UD....//...6I9...UJlD1
...U.08cUuDcU0OuwJPlB9aMW/.6mc..zzzz..UJdtvvzczD6A72QifFzy1...........U.8..E.06.
.wUmc2beYz1.dA8E5Exwz0..........2AcH.wiYG0..8k7gobi0.t/EkGzXL0/k.Et613VqD.233Q1.
jTI5...VzyMgJxyD.mfGNzXpJ.A..XjH1dltzIU.8ED4cY0..gVItYcbK.A8nCWrH1.2.1.0zc.8wz.k
/6U0.wzzz1...................................MPqe0UYdeMezzlz3X8.rE19rExDJO5D.E5W
nVMzTh8em/.UktdbQsbEPt8.3I.06.bTTuYH.Y6IEZ6ly73VE0EFVV4OMw5N/h6.bitgnmqToNOb.o3P
dl4kzdth9/.Lgt0P...cU08czz/cU08cyz1cU08cxz3cU08c.6LMWpWPZ7KRg3a9e/rN............
E....MEJF3E.....I....c....kHXFLM4J5PgZYFH/EM.A3..E4.......................U/4MU/
4M........EAnAnAnAnizMaNaNaN4.zD................................................
................................................................................
.....................A/....3....1....wZIjFLMoJ4.................................
4MU/........................Q40E.......GN.2.......12./..........................
................................................................................
.....................................wzzzzD......MoPgFKOiRKGXxqQV/kR............
..........U/4M...MU/4MU/................................................kz1.....
.......................U4/2.....................................................
................................................zzzzz1......4x4PYZaPbFJNo7LMnE4.
.....................6U.C...4MU/4M.................wz.........zD................
................................................................................
......................................................6....3....3....2YEjVLHjFqG
VlKO.65..........................QU1..........................zj..........kAnAnA
nAnuz.........zDnAnAnAnAfz1.....................................................
................................................................/....E/...U0....
HZKNm/LOiBrOdB1.m/..............................4MU/4MU/........nAnAnAnAvz1.....
...wz.........zD........kz1.............................cz1.....................
............................................................................}
{Titel: golden-pyramid-chillheimer}

[ericr]

an other exemple
Mandelbulb3Dv18{
g.....w...U40...ET.......kEwEfZ8IqNyzGk.gtgCwE1E2YF7MWp2Qz9SWebA32JszMiqammn1Dzj
........................................E.2........Y.FE........E........kz1...wD
...Uz6/..cjE.....wX//...........G5....E4.....omEQgisq6oD.w1.......Ut/xckpr1....6
/F....kD1A../2...........................................EW0/.....2...sD...../..
.w1...sD3Gp1cXn1Ewfo/Y/OPHl8zOn.1Od3VfkDN5ut9YCdXwvPcIHb1TC3zwRWQEkpa8mDcBCi7kBo
Xw9VWdAJkCtoyUBAfycXqImjU.....2G....P/...2UaNalD.2....sD/.G.....................
.............oAnAt1...sDds0./x1...................................kJy0EE1/....x/
.....Ksulz1.......kzJ.6E.2dT.2C.I....M/...EO....i/cR9kB.UK.A....H/...c4n..UG.h56
Yc3U.0.MzzDg./kz...Uz13..Y7.1c..zzzz............6YCpCckYczH...........U.BwDyhrC.
.wUmc2beYz1.dA8E5Exwz0..........7.EF0wzzz1...........U2..........sWP8w.W8zP32YFy
XAm6..UUINWDmqjjR.t/8QJAL.2.uOGL2nnLz4U.8.kzzzD............8....................
/6U0.wzzz1....................................C....wk1Dwzz/..wD.k1DwkvzD.U9...Dw
k1TzTpxe...wk1DwQs5s....k1Dwk1bTU1....Dwk1Dly/C....wk1DwMw5s....k1DwknqTU1....Dw
k1Dkz/C....wk1Dw...s..kEzz/..wD5yz1.s0EPxzJrf0kd.QoErUXAmwZNZ7bPVt4NZdbAk.1Aic4Q
E....ME/F3E.....I....c....EGXxqQVVKNY7rPiZYFH/..n/........................U/4MU/
4M........UaNaNaNat1.pAnAnAnA2zD........kz1........wz........O3E................
................................................................................
..........................kzzzzz......kPYJqMVVKNY7rPiZYFHJ4S....................
.....MU/4MU/4.U......cNaNaNaNW.EOaNaNaNqjz1........wz.........zD................
................................................LYhnrDpstz1........5./..........
.....................................wzzzzD......QaPV75PnEYNVB5R.E4.............
..................U/4MU/.6......vFVf53iSkzXaNaNaNaNizcNaNaNaNavDOaNaNaNaty1.....
...0./.........E...................A./....................gaNaNaNaNizcNaNaNaNavD
........kz1................................0....2....A....EEh3aSdtqNU6oPs/.PY/..
......................k/9.................kzzzzzzzzwz...........nAnAnAnAlz1.....
................................................................................
.....................................................2.....3....5....2IPVdLOiR46
HJbQa/WA.........................Q..4MU/0....................Uzj................
...uz........................................60E................................
................................................................g2...E/....0....
/pKMuZaPb/mIp7bN.A1N........................5.U/4M..0...........lAnAnAnAnz1.....
.....sYMEUJC2i2E..............................................................zD
.............................U.E............................................}
{Titel:    apollo 4}

[jotero]

Hello all  


Thank you “Chillheimer” for the nice camera perspective and “ericr” I work hard on many solutions  


Original http://les-monts.deviantart.com/art/Perforate-Planet-506105560

ciao
torolf

[ericr]

Mandelbulb3Dv18{
g.....w....K0...Y/.........dMUPqyx/..Dd//xcua62EgT/RO6bGVzHNYJcsjUzyz6LHe0wVznzj
........................................kz1........Y./.........E.......U4/2...wD
...Uz6/...Ue.....wn./.....kz....e6....E5.....omEQgisq6qD.w1.....D/U30/.........6
//....kD12U./2.........A./................................U0......2...sD...../..
.w1...sDkBVfA028LuPnEYt5OjD8zw436CbbC0jj04Qv88zrcwf7Kh2mSJpky4xuA.V0HXjjgFdfQY4w
svPiXrmTz64wygZr9IgJ8XmDU.....oS....p1........kD.2....sD..G.....................
.............oAnAt1....E....zw1.........................................L/...k1.
.....Ksulz1.....yzzzEwzzzLEN.s3.H0...62...UM.......06YB..UU1....Q....I1.....w35c
Uk0U.ydelyjeYFnzI3byzDPk.0.102p.zzzz..UXKca4ZdxD6Q/i5cA0tz1.rsNkbjA8.l/.L.UwhPC.
.QzVa8Iecz1..a4GpVHwz.kEXENSiV.k.6U0.wzzz1...........Q8.....................0c..
zzzz.................................2U.8.kzzzD............8....................
/6U0.wzzz1...................................66cZ.EHVMFHF.GoTu2.cxo7cl0EnueM.g5P
Dh5CUVNeu0kF.VnFjtbUUK0.B3W3BNfT00O7.oI6Kooyy76cZ.EHVMFH.xbUUK0.B3W3BFsT00O7.oI6
Koomz76cZ.EHVMFH...crIGJzzFoTuIdyzngi8qdxzZX.4rU................................
E....EkAl2E.....I....E....kLVB5NVp4Jm3aPn/kQaxaQh/...................MU/4.......
...................................................szMaNaNaNaNzD........kz1.....
.............E/E..........UNaNaNaNavz...........................................
......................1....3....D....2YEjV5Ig34RdtKRh/..........................
.Q..4MU/....BAk.1AU...........zD..........k53iSIsuFvz........O2E................
.....Uf53iSIsuuD.....................MaNaNaNatyD................................
................................2....E/...U0....BJaPbJaQn.UQjtKG4B3.gJKOY/......
................4MU/4MU/................6.2........4./........zD........kz1.....
..............................................................................yD
........Uz1........sz.........yD..........E.....I....c....EHZtqNZ7rA..LNm/.Pg/..
..........................U/4MU/4M................U/./.......00E........E.2.....
...wz.........................................................................zD
........................................................}
{Titel: kleinian until infinity}


the image is a prevu version use   1000*1000 or more it is better (256 ko maxi !)

nb :very well jotero

[ericr]

a loxodrome put on a plan , the light make like a stereographic projection.
I have a spiral. Is it possible to have a cornu spiral ? yes, see

http://bugman123.com/Math/index.html

but how ?

[jotero]

Hello all 

kleinian fractal, i keep working hard 


ciao
torolf

[ericr]

wonderfull ( did you use sphere inv or an other method)

I work hard also to find spial wich loxdormi   I have no idea for putting the light

[ericr]

an other exemple of  double spiral but never the good one
I take a ftactal in deviantart and modif it but no ....
I will become  crazy beford If I continu
  

[jotero]

Hello all 

kleinian fractal "no sphere" ericr


 
http://www.evolution-of-genius.de/3d/fractal/kleinian_fractal_sauermann_III.png

ciao
torolf

[ericr]

most wonderfull

you use a polyedron +rotation+ aboxmodkali power -1 ?

[jotero]

Hello all  

amazing box  


somewhat better   Kleinian groups Mandelbox "amazing box"


Zoom in
http://www.evolution-of-genius.de/3d/fractal/kleinian_groups_mandelbox_end_jotero_b.png


and another picture 


ciao
torolf

[ericr]

wonderfull

but  MAY I HAVE THE PARAM  PLEASE or only a tip

I TRY DOING THE SAMEE BUT NOYHING

ERICR

[ericr]

Mandelbulb3Dv18{
g....ET....x/...ET........U1W4M8eNC6.HkttdqZZ3/EVj7HYHcv..w9sVzrw8s5.ZpNTeRvp3/k
................................BOW5zp2jlz1........Y.7/.........nAnAnAnQ5/2...wD
...Uz6...........Q.0/....2......4/.....j.....2nGUhVdAyqD.Q.W9dsD/K3o0dkpXk1.YH/j
/FEnAnQD12../2UNaNaNaN4yzcNaNaNaNazD........qz1..........kU5.....y1...sD...../..
.z1...sDTjm1sh5MixXCpFNuVo9IzsQDZyBqRamjrFUi2U6luwvRbc4hBfGMzQRxhk3v/dqD.mcdCLBK
DxHcf33yWmFOzu.14Crge3qDU.....26....B.........kD.6....sD..G.....................
.............oAnAt1...sD...m0x1....................................W9dsD5....2..
.....Ksulz1.......kz.wzzz5.U..6.P....61...EB....U0...s/....F....6/...A4.....SFD1
...U.0aZczDM6/nzMg2czX6dE16.0c..zrhe...pMnDnNqyD6.Dbqxm4Iz1...........U.8.UQgk0.
.wUmc2beYz1.dA8E5Exwz0........../6U0.YnFP/..fjrwdvgqzs/Fbf24LNyD..........E3l6Iz
y1hS..UntEsqczzD.ujLGRYA/z1.GqgUe0UD.LEAVszz9v3..wCxDe520z98Lx13HPUpz0U1keCrVQ/k
36/3yzDlJ/..y7sgDCRkz..ADOsW3Kxj.YgRrQMAL.A..UTVR..y3q/yzz/k.1A..1Ak.vzDsnwF.UDn
5VTzThdht0kaqaPiQs5y3q/.sLM5s1bTsLM5.UTVRUDlyVTVR..y3q/yMw5y3q/.sLM5snqTsLM5.UTV
RUDkzVTVR..y3q/y...y3q/bzz/k.1Akyz1yATomxzpaqaff.gKSTB4PjJ5Nic4Qb/..............
E....I.B/3E.....I....I....EE0x4SBx4N934Pd/UQ..........................k/C.......
..........U........uzKaNaNaNaNwDoAnAnAnA/.2........../.........E................
................................................................................
.....................E.....3....9....oINiRKNmVISkJaQ............................
.............6...............szD9nAnAnAnC.2nAnAnAnAyzENaNaNaNavDaNaNaNaN8.YaNaNa
NaNvz0........../fQc3NvwRzXyyd4joB7ezoAnAnAnAnyD........kz1.....................
................................0....E/.........T73QjRrA........................
........................................U.2.....................................
................................................................................
..........................................E.....I....I....EE0x4SBx4N934Pd/UQ....
......................k/C..................HrYMEUJCwzCNaNaNaN4xD........kz1.....
...wz.........zD................................................................
.....................................................2.....3....8....AJOZ75QdtqQ
fZqA.................................MU/4MU/4........MaNaNaNaVzjmAnAnAnAG.2aNaNa
Natyz........UyD................................................................
...................wz...................kz1.....................}
{Titel: apolo 20 juillet 15}


i give the param 
it only the 1st