Here goes the images. It's the first time I used deviantart for this so I hope it wound "dissapear".
The power = (4, -4) elazobulb with p norm (radius) of "p" = (2, 2, 3).
Mandelbulb3Dv18{
g....ET....x/...m....26...EB4sS.Kvb0.nmlSTy6tVzDNCDBHyrtYznf08ReszqxzuT4XYihVCzD
................................t2.2We1vjz1........4./..................y.2...wD
...Uz6.....e2....w.0/.....U3/...y.....E5......EboVpA54rD/w........Uy/dkpXm1.BnAH
y.EnAngD16../..........wz.................................U0.....y1...sD...../..
.zHnAnoDGpzRbNCg1yPLPa6PsQnQzGVUUU7nNQkjuXrOfli/bx1PKZPOODoRziErk08xa4sjoIkXCHKl
ix16pB95cOwTz8c6ZEU5pbrDU.....oM6...LL...2....sD.6....sD..G.....................
.............oAnAt1...sD....zIg7........................................m....k1.
.....4iSoz1.......Ei.wzzz5.U..6.Z....61...EB....m....k3...UE....8/...MHB....SL5A
Po2U.WeeryDfp3nz....z1....6.5c..zfjp..UhV8JTUGyD6.bgyNvSczH...........k/8.kdBrA.
..KCQAiZ/.A.XwE7eDZzz0........../FU0.wzzz1...........s/...........6.......E.2c..
zzzz............11...................2./8.kzzzD............8....................
/EU0.wzzz1...................................QQef1EXl/f7slE60jC.tt7eacP3dlBr..bc
lOGUSYTyT0Egl0b7jjGyVj7.cmNSag0Crj7W.29TkNmj3ZqjQ1ESQWe7YQJytz7.cWOSaEYPt5ya.U8b
tNG.rRza60.e0ab7..krS7IJzzFW1tRJyzXEwyRJxzprT9IJ.c5HVlKOnVa98/pF................
E....2..F2E.....I....M....UG7FpL3poLCxJFg3aSj7IRg74.............................
...................2./......../k........Uz1........../.........E........6.2.....
................................................................................
........................}
{Titel: Elazobulb_hands}
1
Zoom on it's "bottom"
Mandelbulb3Dv18{
g....UZ....O/...S....26...k7pi2W4okxzeIYPTi3cHxD32j8IUgqEz96FpXoe/Vsz66CTj1hz4zj
................................MR93tjEWa.2........5./..................y.2...wD
...Uz6.....SP....w.0/.....kS0...9/...2E9.....wFrSbY.lGnD/w........U30dkpXm1.D8QR
y.....cD16../..........wz.................................U0.....y1...sD...../..
.zHnAnoD14klUGsElwPR3bj4Gdh9zC0DPelsl5mjcw26ks0/jwnDyh8WYcm4zeeSx4ehd6njeNV5LOGe
VwXSzalj.iXAzSNMLaLgqmmDU.....IcK...Y//..2....sD.6....sD..G.0...................
.............oAnAt1...sD....zIg7........................................S....k1.
.....4iSoz1.....N.kz.wzzz1kP.U8.h/...61....6....m....c3...E9....j....2Y1....TP52
...U.avrazDjTCszzzzzzzzzz1..1c..rTzx...MarH7iXyD6oa4dabdnzH...........I.8.UF4N2.
.sM93P58iz9.eLISw7kxz0........../6U0.wzzz1...........s/...................E.0c..
zzzz.............0...................2U.8.kzzzD............8....................
/6U0.wzzz1...................................QjX.1kqYltqiC0pey/.P467PanJdscb.kWM
dZK.yRjX.1kqYltqYtrxC0A.PH4bPPfTrv6k.gBNQiBxyRjX.1kqYltqXxrxC0A.PH4bPjtTrv6k.gBN
QiRizRjX.1kqYltq..kxC0wgz60peyldoMJ8CuNQfs3.jyeS................................
E....2..F2E.....I....M....UG7FpL3poLCxJFg3aSj7IRg74.............................
...................2./......../k........Uz1........../.........E........6.2.....
................................................................................
........................}
{Titel: Elazobulb_hands_zoom}
2
Julia set of (1,0,0)
Mandelbulb3Dv18{
g....ET....x/...U0...26...EB4sS.Kvb0.nmlSTy6tVzDNCDBHyrtYznf08ReszqxzuT4XYihVCzD
................................t2.2We1vjz1........4./..................y.2...wD
...Uz6....UQ.....w.0/.....Up/...G/....E4......EboVpA54rD/w........Uy/dkpXm1....U
y.UaNadD16../2.........wz.................................U0.....y1...sD...../..
.z1...sDGpzRbNCg1yPLPa6PsQnQzGVUUU7nNQkjuXrOfli/bx1PKZPOODoRziErk08xa4sjoIkXCHKl
ix16pB95cOwTz8c6ZEU5pbrDU.....INA...IU...2....sD.6....sD..G.....................
.............oAnAt1...sD....zIg7........................................U0...k1.
.....4iSoz1.....xzTi.wzzz5.U..6.Z....61...EB....m....k3...UE....7/...MHB....SL5A
Uo3U.WeeryDfp3nz....z1....6.5c..zfjp..UhV8JTUGyD6.bgyNvSczH...........k/8.kdBrA.
..KCQAiZ/.A.XwE7eDZzz0........../FU0.wzzz1...........s/...........6.......E.2c..
zzzz............11...................2./8.kzzzD............8....................
/EU0.wzzz1...................................QQef1EXl/f7slE60jC.tt7eacP3dlBr..bc
lOGUSYTyT0Egl0b7jjGyVj7.cmNSag0Crj7W.29TkNmj3ZqjQ1ESQWe7YQJytz7.cWOSaEYPt5ya.U8b
tNG.rRza60.e0ab7..krS7IJzzFW1tRJyzXEwyRJxzprT9IJ.c5HVlKOnVa98/pF................
E....2..F2E.....I....M....UG7FpL3poLCxJFg3aSj7IRg74.............................
...................2./......../k........Uz1........../.........E........6.2.....
................................................................................
........................}
{Titel: Elazobulb_hands_julia}
3
Another bulb 5,-5 interpolation 0.9 ;2 ,2, 4 with a texture
Mandelbulb3Dv18{
g....../....1...c....26...kAMuiipQd4.z9aUyivWB.Eu4m2zz1DkyXE9VqOPrdvzsfGuaxGCxyj
.................................M9Zp1kZaz1........5./..................y.2...wD
...Uz6....EJK/...Q.0/....2km3...p.....ED.....UPvdQrQkUqD/Q......BJJJ0dkpXm1.NEbq
y.EnAnQD12../.............................................U0.....y1...sD...../..
.zHnAnoDlOYX9LGdtx1AzGF1TVpDzaFt1vgpm/oDWMiDMhIggwnVOU3yGxoRzkdh3AyXBMqDYkzxW8gX
3xP/S2dIhOQNzuLptigTwQrDU.....I6O/..7X1..2....sD.6....sD..G.....................
.............oAnAt1...sD....zIg7........................................G....k1.
.....83iyz1.......kzxwzzzL.U..6.P....61...EB....m..06k3..U.F....6/...c4.....SH5Q
...U.WeeryDfp3nz3ivmz5dFL06.5c..zfjp..UhV8JTUGyD6.bgyNvSczH...........k/8.kdBrA.
..KCQAiZ/.A/XwE7eDZzzC........../EU0.wzzz1...........k/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................QQef1EXl/9gslE60jC.tt7eceP3dlBr..bc
l4PUSYTyT0Egl0LgjjGyVj7.cmNSci0Crj7W.29Tk3vj3ZqjQ1ESQW8eYQJytz7.cWOScGYPt5ya.U8b
tVO.rRza60.e0a5e..krS7YUzzFW1tROyzXEwyxaxzprT9Yn.wKOiFrEgxKRYJ2SkxaQoxpEjp4QV7LO
E....2..F2E.....I....M....UG7FpL3poLCxJFg3aSj7IRg74.............................
...................3./.......E/kVf53iSIsiz1........wz.........zD........E.2.....
................................................................................
........................}
{Titel: MutaGenBDCC1C8EE62F4B5503C1_Elazobulb_knots}
4
And Lp=1 taxicab space bulb of power 40, -40
Mandelbulb3Dv18{
g.....N....Y/...w....26...EJ5p3ODVgzzy3bhPsOZLxDZm.zu8qtSyv/NZjdK3bozy3bhPsOZLxD
................................61JpBG7yzz1........6./..................y.2...wD
...Uz6....U5.....M.0/.....k6/...N.....E4.....gJ2POIWULqD/..........m/dkpXm1.....
z.UaNadD12../..........wz.................................U0.....y1...sD...../..
.zHnAnoDt8Il2Z6sZx1..........Gmb8ANxf5djT8rcxbo35u1S/REk4i9MzYWS80RvjkpD9JYMi2WO
9uX19Tiohz0Lz0LvTyfVv0qDU.....2g/........2....sD.6....sD..G.....................
.............oAnAt1...sD....zIg7........................................2....k1.
.....4iSoz1.......kz.wzzz1.X.Q6.9....61...kA....m....c3...UF....7/...I1...EdhJ5g
Hw3U.ydelyjeYFnzvm9ZzLWiO16.0c..zrhe..EOf5nlcsxj6.Dbqxm4IzH...........2/8.EBl35.
.o0FIhT67.2.hE2Jv5G0./..........3I13.wqN51../0biMaOyzsVsP8OPAXzD/czYfTLkRzH/pElz
5TtN...LVxTtT1yD.yXjDUIN0.2.WRvgcbtszKEA8oDU.06..YKaZ6Aeiz1858nQJ6Tnz.ERpBK.iAwj
/6V0.2FAZ.............klrlkCx9yj.6wTJHz2Vz1..ozz61U7bck7RD.zzH7.aQW0b2X3mHOs.UZ2
6VJBsczNc.EJcIFJOHpzO04.JlG3JV3P..Dw.IFJJJJbm/.wk1E3JJJJOxLzzXA.aQW0bgvTxzDm.Mm7
8QW..qzz61U7bck7...zzHdwuMVwY4ikvPYybV0XJt4.k1De................................
E....2..F2E.....I....M....UG7FpL3poLCxJFg3aSj7IRg74.............................
..................UD./.......s1E........Uz1........wz.........zD........kz1.....
................................................................................
........................}
{Titel: Lp_Mandelbulb_pow30_p1}
5.
I thing these weird things looks the best in space.
EDIT:
I was wrong. Bulb with positive and negative powers very mutch correspondens to to 2D fractal z= z^n + C / (z - a)^d researched by Robert L. Devaney.
http://math.bu.edu/people/bob/papers.html z= z^2 + c / (z )^2 -> z^2 + c * z ^-2 (with initialisation condition being z=(2*c/2)^(1/(2+2))