kleinian

[ericr]

Mandelbulb3Dv18{
g.....s/...c3.../....I.....dtniO8sjE.Hk2JKTUoBAERTGFie6wMzXaC27q0MX0.BW8lOXPsQ/E
................................KH6JB1PNry1........A.N5.................y.2...wD
...Uz6....UA..../wV//.....Uk....8.....k4......KD7gVKdXsD/w/.......US1dkpXm1....U
z.....kD12..1..........wz.................................U0.....y1...sD...../..
.z1...sDctUzFJ9ucynnNswhvhhBzmGzHQ9gCCoDI19/DMwPxwndpXp9ZD6ezMzhxLqzh4sjEBFMB1zB
/xPBS4vxh/PUzUF5ovkf1WuDU.....oL....5/........sD32....sD..G.0...................
.............oAnAt1...sD....zw1........................................./....k1.
.....4iSoz1.......kz.wzzz1.U..6......s0...EB....j....c3...kF....6/...YJB..EJcF52
...U.avrazDjTCszzzzzzzzzz1..2c..H1Ch............6wyBIC4OWz1...........Y/8..1fk1.
.wUmc2beYz1.dA8E5Exwz0........../6U0.EG7f...mIqp.taszs/pMnDnNqyj.gM3ZaYq1zP.mc..
.Rn9..UAZRBEi7.E.0cXcESLfz1..........2U.8.kzzzD............8....................
/6U0.wzzz1...................................6W6W.U6W6W6AFGbjJ1.RyKBRqfE6XAm.UAm
6XATXptPp.EbjJHbItb6W60.W6W6WUeTW6W6.6W6W6G/z7W6W.U6W6W6Oxb6W60.W6W6WotTW6W6.6W6
W6Wxz7W6W.U6W6W6..U6W6W6ACGbjJXRp02m6XAmfsJbjJXR................................
E....6E.F2E.....I....c....EMh3aSdtqN7NoI.MoI.............................MU/4...
...................wz.........zD...................3./.......E/E........I.InAnAn
Angzz........6.E..................M2./..........................................
........Uz1..........2.....3....B....coPnhYPhg2PZZaP7NoI........................
........06U..................szDnAnAnAnAnyXNaNaNaNavzAnAnAnAnAzDnAnAnAnAvz1.....
...wz........U0E........E.2........2./.......kyDnAnAnAnAlz1..........MaNaNaNaF.E
................................}
{Titel: kleinian jos 5}

[ericr]

test kleinian into z diection !

Mandelbulb3Dv18{
g....UZ...Uk/.../....2U...UiZlArDxA5.r3f8quFRX3EmFyrQQwGEz9bFIfnqYG1.BT2ZQOIEy/E
................................3scGcV4yEz1........A./.................U4/YNaNsD
...k.7....k2.....o51/.....U20...8.....Ei.KKZ.th3jEs/uhsD/o5.......US1pAnAr1....2
/FEnAnQD16U./..........wz.................................U0.....y1...sD...../..
.z1...kDEOEczlSRFxPsZej6tvhOzq5wspicBesDzFWwoyoD9y1Q5GetGDLIzcJrk7/3JNpDOHuW7zqI
KxfvyimQcqcWzIGlEQS4obqDUcNaNwnM....h....2....2E.A....sD..G.....................
..................2...sD....zw1...................................E08S1E/....k1.
.....4iSoz1.......kz.chqO1.U..6......61...EC....m....Y3....F....8/...I1.....TN52
...U.u5e.jhf9Bnqz9OSP9/Sn/665c..RrRr............6.........E..0........o.8.U6W60.
.sM93P58iz9.MmnWK2zwz0........../6U0.wzzz1...........s/...................E.0c..
zzzz.............0...................2U.8.kzzzD............8....................
/6U0.wzzz1....................................Dw...Pgl4PGM.wk1..gl4Pg7/4.cqZ.k4P
glKthsUnp1.gCV0g2q1.eF7.gl4Pg74Kk1D..6cUS6sRfBoZC/.Pgl4P75rELu2.gl4PgduTk1D..k4P
gl42.0Dw...Pgl4P...wk1UpiuW1CLTaWQ3wk1UpRrqELuYR................................
E....2..F2U.....I....w....UGjBrGipmGgJKOiZYFH/...............................6U.
0................6lzz63iSIsuF/uDRxckpX0LazHP3vjgv7DuzcNaNaNatFzDoAnAnAngSz9.....
...G./.........E........E.Yf53iSIsWvzQHW//KtERxDBBjXHF57py9nAnAnAnYvzY1h6PbjT8tj
OaNaNaNKvz1.............}
{Titel: klainian jos. z}

[ericr]

Mandelbulb3Dv18{
g.....S....O/.../....2....kMX5Khbbc1.5Se24qZ3CAEamjr7ByzJ.w/25hpA3qszCscZZNsCs/E
................................HQdECybaKz1......Usk.t..................y.2...wD
...Uz6.....0..../Q.0/.....Ev....b.....E3OTZ0zg.YAVgG7bsD/Q.........m/dkpXm1....U
z.....kD12../..........wz.................................U0.....y1...sD...../..
.z1...sDvYYyqs5k2yvye7g6mbvKz.msR.sOFrrjGkLj6k/9Bx9hx.mxNxLWzasdLZDTRgpj/0671YGN
yxv.8OnicOgGzytU4ZCi1HsDU.....Y0....1.........sD3I....sD..G.....................
.................02...sD....zw1.........................................x....k1.
.....4iSoz1.......kz.wzzzb7U..6.P....61...EB....a/...c3....F....8/...Y1.....Snb0
...U.88DwwDJlyuzznQazb2Zx/c61c..6XAm0..U........6.6..........0........o.8.E8E/3.
.sM93P58iz9.MmnWK2zwz0........../6U0.wzzz1...........s/...................E.0c..
zzzz.............0...................2U.8.kzzzD............8....................
/6U0.wzzz1...................................g.vg1.4isW9R3nj....oF5Ro3ADuzl5.67K
M77d8xDG6/U9MUV96u4U.0..MsW9ioaRuzl5.67KM7N9u/.U..kJHCtYTprzz1..MsW9iEeT.0.U.UV9
ismhz/2..0.4isW9...8CvAbNvXyTwFM2k58CvAbJsbyTwFMrsWOkR4.........................
E6...A..V2E.....I....w....UGjBrGipmGgJKOiZYFH/...............................6U.
0.................Uyz.........zD........kz1........wz.........yD........kz1.....
...8./........zD........E.2........wz.........yD...................wz...........
........kz1..........2.....3....1....w3Jm3aPnlKMoJ4.HBJFm.......................
.....................2........yjbNaNaNaN9.YaNaNaNaNmz0.......EzD................
...../.......UzD................................................................
................................Y/...E/...k/....n3rOjB4OUUGAd.kIHJYA............
........................................4.YaNaNaNaN0./.......UxDnAnAnAnApzXaNaNa
NaNmz..........E........sz1.....................................................
............................................}
{Titel: joskn 1}

[ericr]

sinepow2+joskn

[ericr]

Jotero method and joskn-kleinIFS  



Mandelbulb3Dv18{
g.....s/...c3...ET...2....klCdN4y.x5.T9nwUTV1CAEEuLhWfmIN.oXOU.UA0j5.LEUZo.ydC/E
................................o.3gA6ntHznipKzu7rhY.ho/................y.YaNa/E
...Uz6....EW0.../wX//.....U1/...b/....EfN3pczUwazU0w6pqD/w1........m/dkpXm1.r.ys
z.....kD12U.12UaNaNaNaNvz...........nAnAnAnAny1...........U0.....y1...sD...../..
.z1...sDwOnRVKwA7y1H5/XDNGqRzovDxwhH08rj5FUFoes5.w1WfJZ5PNVUzgHMA0N26QsDG3J55a3p
xx1XoMXkhQxUzms4fKYlIwrDU.....2e/...92...2....sD56....sD..G.0...................
.................y1...sD....zw1.........................................N/...2..
.....4iSoz1.......kz.wzzz1.U..6......61...UB....m....c3...kF....6/...YJB..EJcFb0
...U.avrazDjTCszzzzzzzzzz1..1c..enTg............6wyBIC4OWz1...........Y/8..1fk1.
.wUmc2beYz1.dA8E5Exwz0........../6U0.EG7f...mIqp.taszs/pMnDnNqyj.gM3ZaYq1zP.0c..
.Rn9..UAZRBEi7.E.0cXcESLfz1..........2U.8.kzzzD............8....................
/6U0.wzzz1...................................QjX.1kqYltq570pey/.P467PGxIdscb.kWM
dZq4t/.U...E..sqidrz.0...wDEPnsS.yD..I1bGgBMwZc04/kzz1kqSr5Uz1..sb6ePjeT.0kz.kr5
Iih/zRjX.1kqYltq..kxC0wgz60peyldoMJ8CuNQfs3.jyeS................................
E6...Mk.IJE.....I....M....kLn/5OZ7LNdtaR.IaQ.............................oU30...
..........kAnAnAnAngzmAnAnAnAHyDBnAnAnAnIzXNaNaNaNaxz.........zj................
................................................................................
.....................g.....3....3....2YEjVLHjFqGVlKO............................
.QU1.................wzzzzzzzzyDnAnAnAnAny9........wzAnAnAnAnAyD........kz1.....
................................................................................
................................/....E/....0..../7oPsB3QcJaQZxYNaBLNoF1N........
............5...................OaNaNaNahz1........wz.........zD................
................................................................................
..........................................kC....I.........kLG/rPrBnLoE4.........
...................................................6./..........................
................................................................................
.....................................................2.....3....8....2KPVdLOiRKG
4B3.................................4MU/........................................
.......................UK/2...................................................zD
................................................................/....E/...k1....
8xqQ9tK99lKNdtKG4B3...............................U.06..........BnAnAnAnsz1.....
...wz.........zD........kznAnAnAnAntz.........zD........i.2........wz........./E
NaNaNaNadz1........sz...................kz1..........cNaNaNaNavD............}
{Titel: kleinian into kleinian}

[ericr]

the same as up but joskn-mod

[1Bryan1]

Nice looking objects!

[ericr]

thank   you

[ericr]

kleinian group but  the klein value come's form caculed bianchi group found in arxiv.org
Mandelbulb3Dv18{
g.....w....o0.../....2............U6.1......Uj0E2h6PbjTOCz1S9yTqOSY4./..........
................................nAnAnAnA1z1........A./..................y.2...wD
...Uz6....E8..../w50/.....kP....8.....kb.....IzP28XSPtsD/w5........m/dkpXm1/...U
z.....kD12U.0..........wz.................................U0.....y1...sD...../..
.z1...sDhA25f9iBmx1..........0....................E91lluWPXQz..........U........
.............omEQgisq6rDU.....o4....k....2....sD.6....sD..G.....................
.............oAnAt1...sD....zw1........................................./....k1.
.....4iSoz1.......kz.wzzz17U..6.P....M/...U1....i/...kB....F....6/...I1.....SnD1
...U.0.MzzDg./kz...Uz13...6.1c..zzzz............6YCpCckYcz1..........2k.8.kXWF1.
.sM93P58iz9.MmnWK2zwz0........../QU0.wzzz1...........sF92FpyVY.E.sWP8w.W8zP.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1....................................C....wk1Dwzz/..wD.k1DwkvzD.U9...Dw
k1TzTpxe...wk1DwQs5s....k1Dwk1bTU1....Dwk1Dly/C....wk1DwMw5s....k1DwknqTU1....Dw
k1Dkz/C....wk1Dw...s..kEzz/..wD5yz1.s0EPxzJrf0kdl61Bic4Qb/......................
E.U..2..F2E.....I....w....UGjBrGipGHjFKG4B3..................................6U.
0.........kU.fQc3Nvyz...................Uz1........sz.........zj........Uz1.....
...8./........zD........E.2........wz.........yD...................wz...........
........Uz1.............}
{Titel: kleinian parabolic o 3}

[ericr]

Mandelbulb3Dv18{
g.....I....E/.../....22...URybVZGFU2.zfmaENxaC1EAb27d2Hi2.Y/0Kd0ITo2.nDv8M7k4h/E
................................k1bZhvtZNz1........Y.l5........E........y.2...wD
...Uz6....k0..../w50/.....Us....j.....EbeD7HzEkfNrglI2tD/w5........m/dkpXm1....U
z.EnAngD12U./2.........wz.........zD........kz1...........U0.....y1...sD...../..
.z1...oDPODFxua7EyHKJoPKCY8PzALYxxK332rjthyIITq/muH8kTnnr1WWzwiKppX00MsDJg6cYzwD
qxHIqDOuKwAVza3cdnXEoWsDU.....o2....M....2....sD56....sD..G.....................
.................y1...sD.....w1.........................................R....s/.
.....4iSoz1.......kzxxzzzX7U..6.P....20...EB....M0.06Q2..U.F....6/...I1.....Sn52
...U.0aZczDM6/nzMg2czX6dE16./c..zzzz..EbG7eFT5tj6.BC4POwoz1...........E.8.U9q.5.
.Eot8VlJqy9.3yuedc8tzC........../EU0.wzzz1...........E0...................E.2c..
zzzz.............0...................2./8.kzzzD...........EB....................
/EU0.wzzz1...................................wTq41kxsXDyee0k.1A.PnBrQHJJwXSe.IDv
DLDmxVTVR..zxK6zQs5y3q/.rW7Tr0bTsLM5.sTvRvDlyVTVR..mjx/mMw5y3q/.YSbHYmqTsLM5.kzv
XnDkzVTVR.UwMzfw..EzOjPsee0k.1AkIJ3zdr8uwy5y3q/bnAnBmsWOkR4.....................
E6...ME.G7E.....I....c....EEkx4PgxqA2pGG4B3..............................MU/46..
.....................AnAnAnAnAvDwbOwGrYMcz1.....................................
...2.BmqtvbOwGvDXcoS1y0HazHCoWgRyydoz.........yD...................wz...........
nAnAnAnAHz1..........2.....3....D....coPnhYPhg2PZZaP7NoI........................
........06U..................czD........kz1........wz.........zD........Uz1.....
...wz........U0E........kz1........2./........zD........Uz1...................zD
..........kAnAnAnAnoz...........L....E/...E/..../7oPspoPYhIMgZ4.m/..............
............5s..................7nAnAnAnYz9...................zD........kz1.....
...wz...........................................................................
................................................zzzzz1..........................
...................................................6./..........................
................................................................................
..........................................................kzzzzz................
..............................................................0E................
................................................................................
................................................................M/...E/.........
T73QjRrA................................................................U.2.....
................................................................................
............................................................................}
{Titel: kleinian space~}


backbround : Orion nubelar

[ericr]

Mandelbulb3Dv18{
g....UZ...Uk/.../....2U...Eq7Lkgx7r5.91Iok9jGR1Ex1kHu6fu6.I1/WITuQWA.n0O5uK7c/.k
................................ptu3COV0az1........A.x7................U4/2...wD
.....7.....0.....o51/.....Uj/...8.....EhS5Le/3B/OsxAcIrD/o5.......US1pAnAr1....2
/FEnAnQD16U./..........wz.................................U0.....y1...sD...../..
.z1...kDCsinTpjyoxHqO5Vrm/iCzUztKvb7m2oD2L5X2vusuwHfFZTAD19JzEZDWUV9mFrjjqpHU9CA
/xf.wt8Km65RzochNaHxvDpDUcNaNw1B....D....2....sD56....sD..G.....................
..................2...sD....zw1...................................E08S1E/....k1.
.....4iSoz1.......kz.wzzzX7U..6......s0...EB....j....c3...kF....6/...YJB..EJcn52
...U.avrazDjTCszzzzzzzzzz1..2c..H1Ch............6wyBIC4OWz1..........kY/C6.1fk1.
.I3cB7jWU.2.Dvwxuehwz0kvO61SCD.E/6X0.EG7f...mIqp.taszs/pMnDnNqyj.gM3ZaYq1zP.mc..
.Rn9..UAZRBEi7.E.0cXcESLfz1..........2U.8.kzzzD............8....................
/6U0.wzzz1...................................6W6W.U6W6W6AFGbjJ1.RyKBRqfE6XAm.UAm
6XATXptPp.EbjJHbItb6W60.W6W6WUeTW6W6.6W6W6G/z7W6W.U6W6W6Oxb6W60.W6W6WotTW6W6.6W6
W6Wxz7W6W.U6W6W6..U6W6W6ACGbjJXRp02m6XAmfsJbjJXRrQHCrQX9e/rN....................
E....AU.V2E.....I....c.....Rm3aPnNqPmpKG4B3.H/UFH/.......................MU/46U.
0....................AnAnAnAnAwjBnAnAnAnUz1.......8B./.......6.E................
.............E/E...................wz...........................................
.....................2.....3....7....22Qjl4Pj71FhYYFH/..........................
....4MU/0.................................kAnAnAnAnwz...........................
...............EOaNaNaNady1.......U9./..........................................
................................0....E/...k1....8xqQ9tK99lKNdtKG4B3.............
..................U.06................U2zzXIsuFVf53czopX0LD8QNyDQxckpX0LaznNaNaN
aN0vzUaNaNaNapwj........r.2........3./......../EVf53iSI6jznB742MZ1ppzoowCC3RYIvj
mAnAnAnggz1yxHBSdPGUzcNaNaNaNhzD............}
{Titel: double kleinian}

[ericr]

 Mandelbulb3Dv18{
g.....c....s/.../....22...EO.ADSf7GxzK.MMUUY998EXlSMPNPszyPMD7tqxvguzo2g9qBuhUzD
........................................sz1........Y./.........E........y.2...wD
...Uz6.....0..../w10/...........8.....k4uILT.pmEQgisq6qD/w1........m/dkpXm1....U
z.EnAngD12../..........wz.................................U0.....y1...sD...../..
.z1...oDyvlFFZLJXx1...............................UMTo3kX8oMzM2hvo2.qfmD........
..UFoiHH.Mj8z8q5R/wc0BqDU.....oh....F....2....sD.6....sD.AP.....................
.............oAnAt1...sD.....w1........................................./....2..
.....4iSoz1.......kz.chqOX7U..6......61...kB....m....Y3....F....8/...I1.....Tvj.
...U.u5e.jhf9Bnqz9OSP9/Sn/665c..RrRr............6.........E..0.......6m.Xwj6W60/
.IL93P58iz9..mnWK2zwz0.U........AQEF.wzzz1..sZR6IhqTzslTLYhiP3zD.YH4d62w1zP.0s..
zzzz.............0...................2U.8.kzzzD............8....................
/6U0.wzzz1....................................Dw...Pgl4PGM.wk1..gl4Pg7/4.cqZ.k4P
glKthsUnp1.gCV0g2q1.eF7.gl4Pg74Kk1D..6cUS6sRfBoZC/.Pgl4P75rELu2.gl4PgduTk1D..k4P
gl42.0Dw...Pgl4P...wk1UpiuW1CLTaWQ3wk1UpRrqELuYRlUnBic4Qb/......................
E6..3AE.W6E.....I....c.....IjlKS4x4PYJ2ShALShZYFH/.......................MU/46..
0...............................................................................
.....d2qGooyVY.E........6.IwIXwIv5G0./..........................................
.....................2.....3....D....oINiRKNmZYFHxZET7XRk.......................
.....MU/46U.0.....U..........UyDAnAnAnAnoz1........wz.........zD................
..............................................zD..............................zD
...................wz.........../....E/...k1....8xqQ9tK99lKNdtKG4B3.............
..................U.06..........MaNaNaNazz1........kzYNaNaNaNWyDoAnAnAngdznNaNaN
aNK..pAnAnAnAnzD........g.2........0./......../ENaNaNaNanzHnAnAnAnAsz...........
bNaNaNaNiz1...................yD............}
{Titel: main paras~}

[ericr]

kleinian sphere

[1Bryan1]

Thanks for the formula.
Wonderful things to play with!

[ericr]

Thank you, I try to make suitable Kleinian fractals using for example continuous fractions to find wp / q then the resulting complex number