Talis hybridisation

[Alef]

Talis don't hybridises so easyly and are pretty chaotic. But since I don't doing like others (many amazing boxes) and as tribute to Fractal Explorer I tried to hybridise it.
Any Menger goes first, then Talis, and additional _Folding1 finally produced good results. Menger sponges seems to somehow boxes talis.

Tweak it if you like, it still is pretty raw.

Box of tubular bells

Mandelbulb3Dv17{
W.....N....Y/...w....2.....mli2vGsI1.vb54aWLUW2EyqCjT4EbGz9aCHPf30anz8RPNShbu1xD
................................2cb/wpFQmz1........A./..................y.2.....
................/sU0/....6Eu....i.....E2.....cA3UBxYq9rD/.......Need/dkpXm1....U
z.....kD12../2kAnAnAnAnozAnAnAnAnAxjnAnAnAnAHz1............u1....y1...sD...../..
.w1...sDogJkRcNIfx1dTVgXV7YLzGuMqiwZ3KqD1BcV1JklewPwehzgfPTPzkqE9qzOkQqDf5rpW8GE
ex9cLx64kQOMzaZLJbmVeHqD......oL3.............kD.2....sD..kz....................
.............oAnAr1...sD....z.qRN6..sZV.UWL40.ISN6.stZV..eL40.mSN6......8....k1.
..................kz.wzzz1.U..6.P....61...EB....U0...w.....F....8/...I1.....SF52
...U.0aZczDM6/nzMg2czX6dE16.mc..zrhe..UoK/nl2xvj.sM93P58iz1...........U.8.UQgk0.
.wUmc2beYz1.dA8E5Exwz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................UTVR..y3q/.zz/k.1A..1Ak.szDsnwF.UDn
5/EzThdht0kaqa9.Qs5y3q/.sLM5..bTsLM5.UTVR..lyVTVR..y3q/.Mw5y3q/.sLM5.kqTsLM5.UTV
R..kzVTVR..y3q/....y3q/.zz/k.1A.yz1yAT2.xzpaqa9.................................
E....A....E.....I....Q....EHZtqNZ7LG4B3.rJaQ..............................U/4M.1
Ak.1...............0./........zD........kz1........sz...........................
................................................................................
.....................2.....3....6....EJMgZqQI/5S................................
.........6....................zj........kz1.............................kz1.....
........................U.2.....................................................
................................/....E/...E.....TNoPgFKOiRKA....................
................................D8QxckpXGz9.....................................
................................................................................
............................................}



Zoom in Talis pipes
Mandelbulb3Dv17{
W.....S....O/...w....2....UUizzttBIwzOdMbbJ7Cn.E9LviZmQHfzfZxAQULpauz2aov8mvyXyj
................................LiwOkrtre.2........Y./..................y.2.....
................/M.0/....6.8/...5/....E2.....kdCWcONkKnD/..........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.w1...sD3UJBG/.e1x1gNFjrxut7zo0AixFxAkmj.qvdKe5tatnay4i6pO7EzYsfLButljnDcrZHAjRJ
mwHXTsikXCJCzqiO.rQ9FsnD......oTJ.............kD.2....sD..kz....................
.............oAnAr1...sD....z.qRN6..sZV.UWL40.ISN6.stZV..eL40.mSN6......M....k1.
..................kz.wzzz1.U..6.P....M4...EB....W....k1....F....8/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc..k18XGQeGyD.sIRhrVAkz1............28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../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....A....E.....I....g....EHZtqNZ75B..pPrJaQ................................Ak.1
Ak.1...............0./........zD........kz1........sz.........yD................
................................................................................
.....................2.....3....6....EJMgZqQI/5S................................
.........6....................zj........kz1.............................kz1.....
........................U.2.....................................................
................................/....E/...E.....TNoPgFKOiRKA....................
........................................6.2.....................................
................................................................................
............................................}



Throught i wolud prefare these repeating relict squares. Here is menger4 + tricorn + folded1 hybrid. Zoomed in:
Instead of tricorn can go all mandelbrot type formulas, but folding is nesesary.

Mandelbulb3Dv17{
W.....S....O/...w....2.....S4QkgfO5xzSXcIgzi0wxDBSVdlnySfyvGG92dx22wzcAgIoUFkBzj
................................ET1o2T8DD/2........Y./..................y.2.....
................/s.0/....6Ey....m/....E2.....k9E18jmc8lD/..........m/dkpXm1....U
z.....kD12../..........wz..................................u1....y1...sD...../..
.w1...sD5omsYIeZGwX9X0FrSpZoyU1uwNpKb7hDaybmBswzNvfiqQX8RoX0zsrXDEyJKdkDh8FwFruY
psH8cbPg1.b0zSTgBpOlKdkD......Yy3.............kD.2....sD..kz....................
.............oAnAr1...sD....z.qRN6..sZV.UWL40.ISN6.stZV..eL40.mSN6......I....k1.
..................kz.wzzz1.U..6.P....M4...EB....W....k1....F....8/...I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc..k18XGQeGyD.sIRhrVAkz1............28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../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....A....E.....I....g....EHZtqNZ75B..pPrJaQ................................Ak.1
Ak.1...............0./........zD........kz1........sz.........yD................
................................................................................
.....................2.....3....1....6YQdB5Rj7bEmx4R............................
...............................E........kz1........wz0..................kz1.....
........................U.2.....................................................
................................/....E/...E.....TNoPgFKOiRKA....................
..........................................2........wz...........................
................................................................................
............................................}

p.s.
Maybe some had done this, but maybe not. And maybe it is usefull, maybe not;)

[DarkBeam]

Talis is intended to be used alone

[Alef]

It looks very different from 2D talis. Maybe some coefficients or iteration number, realy hadn't much trayed. Just that crossbreedin is much more fun;)

[DarkBeam]

I agree but you intend "duckytalis" probably...
I have copied this from sam.ufm
There are lots of variations, including rain's ducky and more, they are fine in 2d but... 3d is more challenging

[Alef]

FE talis looks like mandelbrot, so I expected, that in 3D it would look like some 3D mandelbrot;) Anyway, I haven't much used talis 2D formula.

[DarkBeam]

FE talis looks like mandelbrot, so I expected, that in 3D it would look like some 3D mandelbrot;) Anyway, I haven't much used talis 2D formula.

It looks like - only on cut sections too bad.

Here images... Param

Mandelbulb3Dv17{
X.....S....O/...w....2.....WIePgvsWzzipHoQvjMR1ENJ9vXgkA.w1kJfOIx95azi4KzUlH4DxD
................................MaLq7bq8xz1........A./..................y.2.....
................/M.2/.....k./...d.....E2.....QICXtoJvDqD/..........m/dkpXm1/...U
z.EnAnQD12../..........wz..................................u1....y1...sD...../..
.wHnAnYDbsVhARpyXx1..........KTkrFATS/djxel8Hkm33uX3NSJRP1dLz2AWpjImyapDFcea.yV0
7unoctVH7vPKzmsA59rqEupD......YI..............kD.2....sD..kz....................
.............oAnAr1...sD....zU/St4.isZP.MZLi/UTSt4.auZP.sgLi/UxSt4......K....k1.
..................kz.wzzz1.U..6.P....I4...EB....W....k1....1....b....I1.....SF52
...U.qFG9yzb2zzzRYoWzz7lz16.mc..zXCc..k18XGQeGyD/sIRhrVAkz1..........2.28.kFrA0.
.Ub96aAIVz9.1se7Umvxz0........../6U0.wzzz1................................E.0c..
zzzz.................................2U.8.kzzzD.................................
/6U0.wzzz1...................................kzbB.EtLXA.BcVu12..FqvW..e8r5jI.kiv
p1.Nu6O/Q1E9WM/.Rx1j84/.L1fV.gcGYuk/.EuTK/UuJFRwO.k3Gg..j2qWDGA.OuaD.o.P2fiB.AG5
J.kZrhPnU0.ybLB.........ee0.....IJ3.....wy5.....................................
E....2....E.....I....U.....JVlKOnF3Qs/kPrJaQ..................................U.
...................wz0........zD..............................zD................
............../E................................................................
........................}

See the I button to see info on formulas, you get:

Code:

Description:

Talis-like 3D set, based on D. White's new "triplex formulas".
The base are the fast non-trig formulas, reported by Bugman's site.
( http://bugman123.com/Hypercomplex/index.html )

This formula comes from Fractal Explorer, and the D.H. Van den Berghe
Ultra Fractal version made in 2010. Added some "extra" parameters.
Too bad, this implementation does not look good in 3D, because Talis
uses a fractional formula. 2D sections at z=0 still show the original fractal.
Maybe, playing with the parameters you can find something interesting?
Tip. Try to make hybrids with Magnet.
This implementation is by Luca GN 2011

// z = ((a1*z^pow + a2*z + a3*c) / (z + p3d) + (1-a3)*pixel
x1=x; y1=y; z1=z;
i=pow-1;
r1 = sqrt(x*x+y*y);
repeat
// raise z to an int power
r2 = sqrt(x1*x1+y1*y1);
z1' = r2 * z - r1 * z1;
z1' *= zmul;
r2 = (1 - z * z1/(r1*r2));
x1' = +(x * x1 - y * y1) * r2;
y1' = -(y * x1 + y1 * x) * r2;
save y1',x1',z1'
i=i-1;
until i>0;
x1 = x1*a1+x*a2+Cx*a3; y1 = y1*a1+y*a2+Cy*a3 ; z1 = z1*a1+z*a2+Cz*a3 ;
// --- divide by z+p3d
x2 = p3dx+x ; y2 = p3dy+y ; z2 = p3dz+z ;
// ---
R = x2*x2 + y2*y2 + z2*z2 ; r1 = sqrt(x1*x1+y1*y1); r2 = sqrt(x2*x2+y2*y2);
z = r2 * z1 - r1 * z2; z = z / R;
z *= zmul;
R = (1 + z1 * z2/(r1*r2)) / R;
x = +(x1 * x2 + y1 * y2) * R;
y = -(x1 * y2 - y1 * x2) * R;

x += Cx*(1-a3); y += Cy*(1-a3) ; z += Cz*(1-a3) ;

[Alef]

Talis formula works pretty different from Mandelbrot. Was thinking of a rotated surface quaternion.