Apollonian Gasket 3d

[ericr]

after a very very long time  
A Apollonius gasket Cornu Spiral

Mandelbulb3Dv18{
g.....S....s/...ET........kDlHAiJaRvzeAacMGhxj0E5osBg/koXzHmO/vL8JQ/.LthhxjXAimD
................................cYCxHXOgsz1........Y./.........E........y.2...wD
...Uz6/..Ea3.....wE./.....U12...NX....k0.....EyIdBKROSqD/wkNVxsD...m/dkpXm1....U
z.EnAnQD1A../2...........fNaNaNaN4zD..........A...........U0.....y1...sD...../..
.w1...sDYsAIxzzzjz1..........WAbUdisqcljTcFzUvMS3t97C1JzzzzvzUNehUisqcljMaO9c9iB
Ow1mQ0auWPX4zU2bVezzzzyDU.....o50...s/...2.....E.6....sD..G.0...................
.............oAnAt1...sD....zw1...................................kNVxsD92....x/
.....Ksulz1.......kz4.gQskEP.65......E0...kF....Z/dEAI2.kzk/....Z....I1....UJg52
Tc3U.08cU0AcU0eQ.06Us.Ak.H..2c..zzzz..EVjiO8eGyj6QwRAgHzGz9.JzHmWnv4.1G/8.klLS4.
.QwRAgHzWz9.fjrwdvguz0UfzHx6d2yD/AV0.s2IV/...........sFbG7eFT5wD.UD6HyVzgzP6/c..
FJ3O.............0..........hw1ZBGouzKl28sjfg33..EYyf/TwT.A8HE4DALHiz0k1KGS.G2xj
32W1xvI75...FnTsuwy5.1.XSMY7dYwD.IQeUHkzqy9...8cU0.cU08czz/cU08.U08cUuzDU08c..8c
U0OzT/8cU0.cU08cQs5cU08.U08cU0bTU08c..8cU08ly/8cU0.cU08cMw5cU08.U08cUmqTU08c..8c
U08kz/8cU0.cU08c...cU08czz/cU08cyz1cU08cxz3cU08c.IKPjtWMh/5.g3aQdFLST3XBs.1Sl.HB
E....MEJF3E.....I....A....kLI7LMiB5PVFLN..UQ....................................
...................wz0....................EnAnAnAnAwzoAnAnAnA1zD................
................................................................................
.....................2.....3....A....wJHj7KOpB5JkV5.............................
..............................zD.....................cNaNaNaNawj..........2.....
.....cNaNaNaNawj..........A..........QxckpX0LD/EOaNaNaNadz9.....................
................................/....E/...k.....TFZQVtqQg34RZ/..m/..............
..............................................................zDBnAnAnAnkzHnAnAn
AnAwz...........................................................................
................................................zzzzz1..........................
...................................................6./..........................
................................................................................
..........................................................kzzzzz................
..............................................................0E................
................................................................................
.................................................................0...E/...E/....
/7oPspoPYhIMgZ4.m/..........................5s..................BnAnAnAnkz9.....
..............zDBnAnAnAnkzHnAnAnAnAwz...........................................
............................................................................}
{Titel: kleinian_groups_02}

[jotero]

Hello all 


out working very nice ericr 

Apollonian Fractal „Toros“


ciao
torolf

[ericr]

kleinian group + volm light

[jotero]

Hello all 

Kleinian 


ciao
torolf

[ericr]

apollonian gasket "paving" a sphere

Mandelbulb3Dv18{
g.....S....s/...ET....6..../.gyqm8I1y0.......U.EenwS1b7r1zPZsJDXitl..ft/iwnfRLvD
.................................2IXYUMU8/2........Y./.........E........o.2...wD
...Uz6/..E4......wX./.....Ek....0W....U1.....At2bZZMxLlD/wnNVxsD...m/dkpXm1....U
z.....sD1AU./2...........fNaNaNaN4zD..........A...........U0.....y1...sD...../..
.w1...sDmZhXL7KzJw1..........u2SkoqZ16YjAcr4f4uUhpfQNvsJWpT3z2mbhiqZ16YjUwNffRt.
0t1Is/HPLCUEyQpbqKZMxLlDU.....2T/...a8.........E.6....sD..G.0...................
.............oAnAtnkpXeDLWeAzw1...................................kNVxsDET....x/
.....Ksulz1.......kz4.gQskEP.65......E0...kF....Z/dEAI2.kzk/....Z....I1....UJg52
Tc3U.08cU0AcU0eQ.06Us.Ak.H..2c..zzzz..EVjiO8eGyj6QwRAgHzGz9.JzHmWnv4.1G/8.klLS4.
.QwRAgHzWz9.fjrwdvguz0UfzHx6d2yD/AU0.s2IV/...........sFbG7eFT5wD.UD6HyVzgzP6/c..
FJ3O.............0..........hw1ZBGouzKl28sjfg33..EYyf/TwT.A8HE4DALHiz0k1KGS.G2xj
32W1xvI75...FnTsuwy5.1.XSMY7dYwD.IQeUHkzqy9...8cU0.cU08czz/cU08.U08cUuzDU08c..8c
U0OzT/8cU0.cU08cQs5cU08.U08cU0bTU08c..8cU08ly/8cU0.cU08cMw5cU08.U08cUmqTU08c..8c
U08kz/8cU0.cU08c...cU08czz/cU08cyz1cU08cxz3cU08c.IKPjtWMh/5.g3aQdFLST3XBs.1Sl.HB
E....MEBF3E.....I....c....kL1xaPYZ2RXxKRiFrIrVZA.U4..................6U.06U.06U.
06................EK./......../E...................../........zD........6.2.....
...0./..................6.2........../..........................................
.....................2.....3....A....wJHj7KOpB5JkV5.............................
..............................zDBnAnAnAnox1..........cNaNaNaNawj..........2.....
.....cNaNaNaNawj..........A..........QxckpX0LD/EOaNaNaNadz9.....................
................................/....E/...k.....TFZQVtqQg34RZ/..m/..............
................................tE9mqtvbqz9.....................BnAnAnAnkzHnAnAn
AnAwz...........................................................................
..........................................E.....I....A....kLI7LMiB5PVFLN..UQ....
................................................................tE9mqtvbqzHnAnAn
AnAwzoAnAnAnA1zD................................................................
..........................................................kzzzzz................
..............................................................0E................
................................................................................
.................................................................0...E/...E/....
/7oPspoPYhIMgZ4.m/..........................5s..................BnAnAnAnkzvAnAnA
nAX..1........zDBnAnAnAnkzHnAnAnAnAwz...........................................
............................................................................}
{Titel: kleinian_groups_03}






http://arxiv.org/abs/0707.2427 :   it is the adresse of a PDF document "An extension of the Maskit slice for 4-dimensional Kleinian groups",
with fomulas and examples but impossible to do the same !!! ( for me).

I try, try but nothing ,  I m sure it MUST BE POSSIBLE to do with mandelbulb 3d.

[/b][/i]

[ericr]

kleinian fractal + volm light + test of Koebe  therom (after riding a text from JOS LEYS)

I hope u like !

[jotero]

Hello all 

Apollonian Sphere + HyperMenger.

|

|



ciao
torolf

[ericr]

wonderfull !

an exemple of inversion hypermenger

Mandelbulb3Dv18{
g.....w....k1.../2....Q...kFoKOIS/w0.5ESy1Evr13EfXP0gdWOozX1XU2Qqkhwzqi11GrH2BzD
................................1LMlmpM.jz1........Y./..................y.2...wD
...Uz6....E9.....wl//.....kE/...O4....Eb.....AfDi93LA9qD.w/........G0dkpXm1.8Qxc
w.....kD12U.02kfZF1G0/yvzghBVXt8M.zDJs28dxj0kz1...........U0.....y1...sD...../..
.z1...sDYacj6Uh8jxHcrCoxoNlKzYDK3x6DJ.qjTXTjd3qpHuHMmnsYY3APzAtctUaOsUqDzn07Yye/
ZxXOR32eUF/Nz8ZB97IJKTqDU.....Yj3...7/...2....sD.6....sD..G.....................
.............oAnAt1....EMm4Vyw1........................................./2...k1.
.....Ksulz1.......kz.wzzz1.U..6.m....61...EB....m....MB....F....6/...I1.....SFz1
...U.ydelyjeYFnzTeOgzf8No.6.1c..zzzz..EizccZWGyD6EdGkxmWcz1...........k.8.kXWF1.
.sM93P58iz9.MmnWK2zwz0..........J2U0.wzzz1..wIUaQ5FazuV4SIRIyUvD.gICycTx2zP.2c..
zzzz.............0...................2./8.kzzzD............8....................
t.U0.k.1A...M4n5/A7mz0kYEkti4xwj..............uBZ.U7EgU7zzFoTu2.oQm2oszDnueM.YXB
bYHzTt6Ul/k6Ukl6Qs5crI0.a.l0a.bTUSH7.M029M0ly/uBZ.U7EgU7Mw5crI0.a.l0akqTUSH7.M02
9M0kz/uBZ.U7EgU7...crIGJzzFoTuIdyzngi8qdxzZX.4rU................................
E....MEBF3E.....I....M....kLn/5OZ7LNdtaR..UQ.............................oU30...
...........................................nAnAnAnezz.........zj..........2.....
................................................................................
.....................2.....3....6....w3OZlKOn/LOm34P.waQh/......................
4MU/..U.0....6....................................QB.Vf53iSIsutD.......aOz1.....
..........................Uyyd4joB7ezoAnAnAnAnyD........kz1.....................
................................A....E/...k0....BJaPbJaQ6Z5QZ75.m/..............
........................0.......BnAnAnAqZz1........wz.........zD........Uz1.....
...../....................k7lU.fQc3pzcjTel9RHWuDBnAnAnAngz1........wz...........
...........................................2....I....I....EE0x4SBx4N934Pd/UQ....
......................k/C.........U................wzeNaNaNaNavD........kz1.....
...wz.........zD................................................................
..........................................................kzzzzz................
..............................................................0E................
................................................................................
................................................................./...E/.........
T73QjRrA................................................................U.2.....
................................................................................
............................................................................}
{Titel: inv hyper menger apollo}

[ericr]

other example

[ericr]

Mandelbulb3Dv18{
g.....8....c....61....2...E1CneLrB.2.LQsdTgWy.5EjM5g2B9uRzH9pouwaDvxz4l.JDVL3LzD
................................971SwQl.fz1........Y.p/.........BnAnAnAni.2...wD
...Uz6...../.....wn./...........x/....Eb.....gWuWCrvi.tD/w1W9dsD/K3o0dkpXk1....E
.FEnAngD12U./2.........wz.........zD........kz1...........U5...../2...sD...../..
.z1...oDhijaPMcGjxHlqWcQP23IzscH1yTCPMmj2FClGuZnswPTMYXKY77MzsF.uHR/ViqD28xH3yvf
CxnCpmtGMEdOzip0LgxTB1qDU.....I/....2....2....kD.6....2E26O.....................
.............oAnAt1...2ExxHjyw1....................................W9dsDB....UA.
.....Ksulz1.......kz.wzzz5../........M/...UE....i/...kB....F....6/...A4.....SF5.
...U.0.MzzDg./kz...Uz13...651E//zzzz..k6ZAOFVE2E62I0FkMpR/Q.13Ml3K0J.lY/V6.vpjD.
.6X7R402g.2.W.4MUtkG.1UPqnM7p32EJ2U0.wzzz1..wIUaQ5FazuV4SIRIyUvD.gICycTx2zPA/c..
zzzz...uoHNriQ.E.mTqayp9/.A..qgUe0UD.LEAVszz9v3..wCxDe520z98Lx13HPUpz0U1keCrVQ/k
t.U0.k.1A...M4n5/A7mz0kYEkti4xwj..............C....wk1Dwzz/..wD.k1DwkvzD.U9...Dw
k1TzTpxe...wk1DwQs5s....k1Dwk1bTU1....Dwk1Dly/C....wk1DwMw5s....k1DwknqTU1....Dw
k1Dkz/C....wk1Dw...s..kEzz/..wD5yz1.s0EPxzJrf0kd.gKSTB4PjJ5Nic4Qb/..............
E.E..MEJF3E.....I....E....kLWx4SoZ4PdtqN.E1N.o4.................................
...................3./.......E/E........I.2...................zD........Ez1.....
...sz...........................................................................
..........................kzzzzz......ENiRKNmVISkJaQ............................
.............6.......YNaNaNa/Hzj..........oAnAnAnAnzzQaNaNaNatzDOaNaNaNazz1.....
..U../..........orDpsZi7FzXyyd4joB7ezoAnAnAnAnyD........kz1.....................
................................8....E/...E/..../7oPspoPYhIMgZ4.m/..............
............5s..........................oz9........kzOaNaNaNatyD........kz1.....
...wz...........................................................................
..........................................E.....I....Q....EE0x4SKBpIc34QZB5.....
......................k/..U.......................U2.XNaNaNaNawjBnAnAnAnYz9BnAnA
nAz9.1......../E........szH5OFqCTzItz...........................................
.....................................................2.....3....B....AJOZ75QdtqQ
fZaFpl4P.............................MU/4MU/4...0..............k........kz1.....
...wz.........zD..................cN./.......O3E................................
...............................E................................/....E/.........
T73QjRrA................................................................U.2.....
................................................................................
............................................................................}
{Titel: apollo 333}

[jotero]

Hello all 

Apollonian Sphere + HyperMenger „Mandelbulb3D ALPHA 1“


ciao
torolf

[ericr]

into a negative power to a box

[ericr]

next  example same box

[ericr]

apollonian deforme by a lens into a sphere optic + volm light

[jotero]

Hallo all  

finding kleinian_groups is not difficult but to isolate them already.
http://www.evolution-of-genius.de/kleinian_groups.png
or hyperbolic 3d !?

ciao
torolf