Jesse I found the original thread by msltoe;

http://www.fractalforums.com/theory/juliabulb-with-'octahedral'-transform-~-sphereflakeHe said

if (x*x<y*y) {d=x;x=y;y=d;}

if (y*y<z*z) {d=y;y=z;z=d;}

if (x*x<z*z) {d=x;x=z;x=d;}

That is a discontinue operator; but if you use the standard _foldingoct instead, you get a fractal continuous everywhere, with the same julia sets at y=z=0 and continue julias!

x=abs(x), y=abs(y), z=abs(z);

if (x<y) {d=x;x=y;y=d;}

if (y<z) {d=y;y=z;z=d;}

if (x<z) {d=x;x=z;x=d;}

Mandelbulb3Dv17{

V.....S....O/...w....2A....OltzAg8.1.PcgNNh9.12Eh3MH9QX/sz11t6QmRkD..D4Iqggq3UzD

................................OaNaNaNadz1........A./..................y.2.....

................/M.0/....6Em....i0....E2.....QzIXLua2PrD/..........m/dkpXm1.BnAn

x.....kD12../2k7080wccYgzSdQgpKtUtzj.......................u1....y1...sD...../..

.wHnAnYD0TkGwYE4kxXTwEcfI0aayqthKy1rN.rj6xCwI1HlaxnwvlQKxa/QzUgWCQqA1PqDnegjT1Hl

axnzpvq6cY/QzKuHN/Lq2PqD......2O..............kD.2....sD..kz0...................

.............oAnAr1...sD....z.MRg4.6qlO..P5f/.qRg4..slO.UW5f/.ISg4......O....k1.

..................kz.wzzz1.U..6.P....M4...EB....W....k1....F....8/...I1.....Sl42

...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1..........2.28.kFrA0.

FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..

zzzz.................................2U.8.kzzzD.................................

/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR

S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq

40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................

E....6....E.....I.........kL4x4PYZaPbxoMo/......................................

...................6./..........................................................

................................................................................

.....................2..........0....YYPoJqNZ756ExqRZ75.........................

8..............................E........kz9.....................................

................................................................................

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

Ah, also another wonderful fractal I found, nearly identical to Xenodream's formula but faster; _absz + CosPow2.

Mandelbulb3Dv17{

V.....S....O/...w....2...............1.......s1E................................

................................OaNaNaNadz1........A./..................y.2.....

................/M.0/....6Uh....b0....E2.....QzIXLua2PrD/..........m/dkpXm1....U

z.....kD12../2UAUATsL5YxzKJACgtgH5xDUDGEfVmwez1............u1....y1...sD...../..

.w1...sDRwPRxQEcaz1aEEXqc/.szEz95uO/yzxDD5a.gaQWGwXnuSV48.etzmPvooeAVOyDb3Cj9K1c

azHaEEXqc/.szahk4lq8..yj......25..............kD.2....sD..kz0...................

.............oAnAr1...sD....z.MRg4.6qlO..P5f/.qRg4..slO.UW5f/.ISg4......Q....k1.

..................kz.wzzz1.U..6.P....M4...EB....W....k1....F....8/...I1.....Sl42

...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1..........2.28.kFrA0.

FWb96aAIVzvh1se7Umvxz0........../6U0.wzzz1................................E.0c..

zzzz.................................2U.8.kzzzD.................................

/6U0.wzzz1...................................2CcN/UvNP6.eeWCNq0.yRii.EJJUk1f..XR

S1.mx3CcN/UvNP6.QsLsUa3.ibhV..bTV1OK.sSq40.ly3CcN/UvNP6.MwLsUa3.ibhV.kqTV1OK.sSq

40.kz3CcN/UvNP6...EsUa3.eeWCNq0.IJ36wk8.wyLsUa3.................................

E....6....E.....I....2....kL/7qQO/..............................................

................................................................................

................................................................................

.....................2.....3..../....AoPnZaPZ/pPr71..65.........................

....06U.06U.06................zD..........2........wz0.........E................

..U7./..................................................kz1.....................

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

If you don't mind I can translate in working formulas all of it for you.