Custom formulas & transforms - WIP & discuss

[DarkBeam]

DarkBeam, you asked for inverse toric coordinates?

Well, I asked WA in case of the "flat" torus, which is a 4D object.
http://www.wolframalpha.com/input/?i=solve+{w%2cx%2cy%2cz}%3d{r*cos%28u%29%2cr*sin%28u%29%2cp*cos%28v%29%2cp*sin%28v%29}+for+{r%2cu%2cp%2cv}&incParTime=true

If you use the same approach for a "3D" torus, e.g. a doughnut-surface, you should easily get the corresponding results from WA that way as well

An entire page of formulas pops out, I'm very confused, what is the correct one?

[kram1032]

I fear, all of them.

It's like solving a quadratic formula but more complex.
Note, that most of them are just sign shifts of each other.

My guess is, that this is due to the fact, that a torus is a finite structure, which repeats after a so-and-so-long straight path...

[DarkBeam]

I fear, all of them.

It's like solving a quadratic formula but more complex.
Note, that most of them are just sign shifts of each other.

My guess is, that this is due to the fact, that a torus is a finite structure, which repeats after a so-and-so-long straight path...

Okay ... It's better to leave toric transforms as they are. It's a fractal program after all Thanks Mark!

[kram1032]

maybe it actually doesn't matter, if I think about it again:

it's like this: a quadratic equation has two solutions because x^2 = (-x)^2

these toric equations have a total of 16 solutions, because the back transform maps all those to the same point.

Also, don't forget, I used there a flat 4D map of a torus... if you wanted a 3D transform, you gotta use 3D-toric coordinates instead^^

[DarkBeam]

Updated database with Ikenagabulb.

[Sockratease]

Updated database with Ikenagabulb.

So why is that zip file still called "Final" then?   

It's never going to be final   

Call the next one "Current" or something   

Just joking.

Thanks for these.  Too many to keep up with! 

[DarkBeam]

Updated database with Ikenagabulb.

So why is that zip file still called "Final" then?   

It's never going to be final   

Call the next one "Current" or something   

Just joking.

Thanks for these.  Too many to keep up with! 

I'm too lazy to change the title    

(And now added all conj formulas. The cheapest update ever   )

[Sockratease]

Is there a reason I get this error message every time I try the "Reciprocal x"  (actually - it's many of the new formulas, not just one) formula:



Could it be a GPU issue?

The 'puter I'm using in this case has no graphics card at all, just the chip-thing it came with  (I use garbage computers for online purposes).  Haven't tried it on any other 'puters yet, but it's 100% consistent on this one!

[0Encrypted0]

Access violation fixed in 1.6.9.4

Edit3:
Update to v1.6.9.4:
- fixed a bug in v1.9.6.3, freeing formulas, rendering, selecting new formula + render again could lead to an access violation.

[Sockratease]

Access violation fixed in 1.6.9.4

Edit3:
Update to v1.6.9.4:
- fixed a bug in v1.9.6.3, freeing formulas, rendering, selecting new formula + render again could lead to an access violation.

Oops!   

Guess I need to upgrade to the new version.

Thankies.

[scheven_architect]

<Quoted Image Removed>

_Sin4Dplus released.

Detail of a _flipxy, _sin4D, CommQuat sequence.

This version of sin() formula is different from UF sin, but I don't know why since should be the same (in slices z=0)

Could I have the settings to play with them? I find it hard to get parameters that give a similar result.

greetings!

[DarkBeam]

Could I have the settings to play with them? I find it hard to get parameters that give a similar result.

greetings!

Effectively, the original sin4d is no longer in the database (was wrong!) and the sequence I told back gives a tricorn but these params can be cool to explore, especially Julia sets


Mandelbulb3Dv16{
O.....S....O/...w....2I..............1.......s1E................................
................................OaNaNaNadz1........A./..................y.2.....
................/M.0E....6kp....J1....E2.....QzIXLua2PrD/..........c./...w1/BnAn
x.....sD1E../.kSNzGNAnlSzcSZpbW3wBxj2C6MhBljbz9..................y1...sD...../..
.w1...sDYsAIxzzzjz1..........UAbUdisqcljp1IDqOBWGwXgZflfm2etzYvqlUV0UOyD85a.gaQW
GwnouSV48.etzSPvooeAVOyD......YJ......................sD..kz0...................
.............................ULRR4.2qpN.cOLb/.oRR4.qrpN.kVLb/UESR4..............
.....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............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....E....E.....I.........kL4lKOkVJK..pPrJaQ.........................c..........
...................6./........zj................................................
................................................................................
.....................2.....3....3....wpIdt4B2/5PpB5..YZK........................
.....................wFVf53iSYzD........................................kz1.....
..............zj................................................................
................................/....E/.........TBqPid4B2/......................
........................................U.2.....................................
................................................................................
..........................................E.....I....I....kEjpKPFJLMo/kPo/UQ....
...................................................wz.........zD........kz1.....
...wz...........................................................................
........................................................}


Mandelbulb3Dv16{
O.....S....O/...w....2....keH28jzhmmzSrpzwoa4Y/E799FSNx2EzvnjUo01bdsz.3rOsXiNduj
................................jDrL.nuss.2........A./..................y.2.....
................/ME/E....6EL0...o4....E2.....6hblPk/fRmD/..........c./...w1.BnAH
y.....sD1E../.kSNzGNAnlSzcSZpbW3wBxj2C6MhBljbz9..................y1...sD...../..
.w1...kDMWfy2QkObw1..........YE.b146jAZjYlykZz869tX932sNAy66zgKmDgpgC0mDVPNF.CV6
9t1pOB5Lnu66z0NMRM4XD0mD......2r0.....................sD..kz0...................
.............................ULRR4.2qpN.cOLb/.oRR4.qrpN.kVLb/UESR4..............
.....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............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....E....E.....I.........kL4lKOkVJK..pPrJaQ.........................c..........
...................6./........zj................................................
................................................................................
.....................2.....3....3....wpIdt4B2/5PpB5..YZK........................
................................................................nAnAnAnAnz1.....
..............zj................................................................
................................/....E/.........TBqPid4B2/......................
........................................U.2.....................................
................................................................................
..........................................E.....I....I....kEjpKPFJLMo/kPo/UQ....
...................................................wz.........zD........kz1.....
...wz...........................................................................
........................................................}

Another interesting combo with a sine ...

Mandelbulb3Dv16{
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................................bV45GzV93/2........A./..................y.2.....
................/ME/E....6Ep/...33....E2.....gaUm14u2ilD/..........c./...w1.BnAH
y.....sD1E../.kSNzGNAnlSzcSZpbW3wBxj2C6MhBljbz9..................y1...sD...../..
.w1...kDmqFnMWolFwX/oui5/Da/zsdtwqX345lDtd.m39Lezv1vnKz0YCG4zmR.gHgNeyjDjE6Vw1ER
HwHTaCcMl4yDyK8fhV..qBlj......Yj......................sD..kz0...................
.............................ULRR4.2qpN.cOLb/.oRR4.qrpN.kVLb/UESR4..............
.....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............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....I....E.....I.........kL4lKOkVJK..pPrJaQ.........................c..........
...................6./........zj................................................
................................................................................
.....................2.....3.........wpIdtKK..5PpB5..YZK........................
................................................................nAnAnAnAnz1.....
..............zj................................................................
................................/....E/.........TN2Pd/5KN/......................
........................................U.2.....................................
................................................................................
..........................................E.....I....2....kLHBKMgZaPb/..........
...................................................../..........................
................................................................................
.....................................................2.....3....3....AoPhpKIp34R
.w4R.65.......................................................zD........kz1.....
...wz.........zD................................................................
................................................................}



And a squarry Julia with her small childs (used the Julia pick to find the seed, do it )


Mandelbulb3Dv16{
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................................nw.rOPHQo.2........A./..................y.2.....
................/ME/E....6kk/...U2....E2.....2XzmrrB1mmD/..........c./...w1.BnAH
y.....sD1E../2kOcoSV5TvoziraN6XEhAvD0kPeVVYMHw9..................y1...sD...../..
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LtH9xRsg2ipJyUmMeYrB1mmD......oO......................sD..kz0...................
.............................ULRR4.2qpN.cOLb/.oRR4.qrpN.kVLb/UESR4..............
.....................wzzz1.U..6.P....M4...EB....W....61....F....8/...I1....UJl22
...U.iVFwxDE./ozPM2Tzz7lz16.mc..zXCc.El18XGQeGyDjvIRhrVAkz1............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....I....E.....I.........kL4lKOkVJK..pPrJaQ.........................c..........
...................6./........zj................................................
................................................................................
.....................2.....3.........wpIdtKK..5PpB5..YZK........................
................................................................nAnAnAnAnz1.....
..............zj................................................................
................................/....E/.........TN2Pd/5KN/......................
........................................U.2.....................................
................................................................................
..........................................E.....I....2....kLHBKMgZaPb/..........
...................................................../..........................
................................................................................
.....................................................2.....3....3....AoPhpKIp34R
.w4R.65.......................................................zD........kz1.....
...wz.........zD................................................................
................................................................}

[DarkBeam]

Updated some c-swapping formulas, test image and render : http://lucagn.deviantart.com/art/Dreams-207889511

[Kali]

Updated some c-swapping formulas, test image and render : http://lucagn.deviantart.com/art/Dreams-207889511

I'll look fot it later, but what I'm needing is the possibility of exchanging cx, cy, cz values to experiment with my new formula.
I do it with flips but I have to do two flips, one for Z & C and another for Z only to restore the values...
(I don't know if I'm saying it clearly)
a total swap of C values in only one step should be nice...

As always, thanks for sharing your efforts!

[DarkBeam]

Updated some c-swapping formulas, test image and render : http://lucagn.deviantart.com/art/Dreams-207889511

I'll look fot it later, but what I'm needing is the possibility of exchanging cx, cy, cz values to experiment with my new formula.
I do it with flips but I have to do two flips, one for Z & C and another for Z only to restore the values...
(I don't know if I'm saying it clearly)
a total swap of C values in only one step should be nice...

As always, thanks for sharing your efforts!

Flipc-xyz; tried? makes this
x<->Cx
y<->Cy
z<->Cz

Or you need:
Cx<->Cy
?