Better later than never, Eric
-
As discussed in dA here a few more details on my pseudo Newton picture made with an JIT formula.
I wanted fast results, honestly, and ignored any mathematical correctness, and many of the discussions here in the forums (sorry to the community
).
Therefore I have made a very simple approach, and said that 1/(t^p) = t^(-p) also for triplex numbers.
The result was better than expected - but actually not 3D.
I simply could see a classical Newton in a cut.
Nevertheless I want to share. Promised is promised :-)
I have attached the formula JIT_gnj_RealPowerPseuNewt3_02.m3f -
you can see it's simply a RealPower turned to t(n+1) = t(n)*(p-1)/p - c*[t(n)^(1-p)]/p
To be more exact it needs: cut at z=0, coloring = Rout angle x,y, and a map color map with its. trap
That's it.
Params:
Mandelbulb3Dv18{
g.....K0...05...S....I....UTcTBr0kRszyUQmDqTqa/EYO8vVTbLbz1DGl8ZbTvsz24a6YMF76wD
................................X20EQ3itK.2........A./..................y.2...wD
...Uz6...........M.0/.....Uj....M0....E4.....I/o6CqCQFmD/.........Uy0dkpXm1/...c
./EnAnQD16../2EWfXLKA4Erzczz.DjOpnxD/NPwnKMSwx1...........U0.....y1...sD...../..
.z1...kD.XqnVT1szwfhkZhoQkwEzktvDxA96JkDQw1moOb1xwP3R1AfblNCzWJdkxSE10oDo7VpZ4o/
vwH4863D1bmAzIhDORn0GBoDU.....o2/.............sD.6....sD0.G.....................
.............oAnAt1...sD....zw1.........................................S....k1.
.....CnAnz1.......kz/wzzz1.U..6.P....g6...EB....I..m3A1.U1U3....8/...YH4...aCRD0
Gw4U.qFG9yzb2zzzRYoWzz7lz16.pc..zXCc...8YqFpt/zD6EBqwnQahz1............2mwzFrA0.
.Ub96aAIVz9.1se7Umvxz0........../EU0.wzzz1...........Y/...................E.2c..
zzzz............g/...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E....2..F2E.....I....2....UG7FpLbtaOT7JNVl4IjRLNm/pQZJbHZR5Rnw3Am...............
...................6./........0E................................................
................................................................................
........................}
{Titel: NewtTest-Outside}
The 'original' picture at dA
uses a slightly different formula (based upon the IQ bulb formula delivered with M3D v190).
If you switch on inside rendering you get some 3D feeling. Howerver it's SLOW and the DE is weird:
Params:
Mandelbulb3Dv18{
g....si...kA0...S....I....kmb06JR6xszqGfHUTHSf/E1ZBAv/jodzXSS1qoxJLtzcltwEYb7.xD
................................7hvtH8fNG.2........A./..................y.2...wD
...Uz6...........M.0/.....kfX...x/....E5.....A5SLshe3FoD/.kAnAnD..250pAnAr1/...m
z2EnAnID16../2EWfXLKA4Erzczz.DjOpnxD/NPwnKMSwx1...........U0.....y1...sD...../..
.z1...kDRxcCZU78pwvZvOkguUYCzom4b4Fm.ljDuJj0p5MGnwvEsJpc1.EAzi.VSqJwfLnDND/OmsBw
lwn0tIc7n0L8zMqHXxC9aanDU.....2FL5............sD.6....sD0.G.....................
.............oAnAt1...sD....zw1...................................krD3yDR....k1.
.....CnAnz1.......kz/wzzz5EV..6.51...66...E9....m..W4o1.UHU3....8/...6H4....SBDG
Fw4U.qFG9yzb2zzz/Qk7znysV16.pc..zXCc..UAZRBEi7yD6A72QifFjz1............2mwzFrA0.
.Ub96aAIVz9.1se7Umvxz4........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E.U..2..F2E.....I....2....UG7FpLbtaOT7JNVl4IjRLNm/pQZJbHZR5Rnw3Am...............
...................6./........0E................................................
................................................................................
........................}
{Titel: NewtTest-Inside}
Last, but not least an overview.
At the lower part of the picture below you can see what happens for larger values of z. So the classic picture is there just for small x/y/z.
Params:
Mandelbulb3Dv18{
g....si...kA0...S....I....kmb06JR6xszqGfHUTHSf/E1ZBAv/jodzXSS1qoxJLtzcltwEYb7.xD
................................7hvtH8fNG.2........A./..................y.2...wD
...Uz6...........M.0/.....kfX...x/....E5.....A5SLshe3FoD/.kAnAnD..250pAnAr1/...m
z2EnAnID16../2EWfXLKA4Erzczz.DjOpnxD/NPwnKMSwx1...........U0.....y1...sD...../..
.z1...kDRxcCZU78pwvZvOkguUYCzom4b4Fm.ljDuJj0p5MGnwvEsJpc1.EAzi.VSqJwfLnDND/OmsBw
lwn0tIc7n0L8zMqHXxC9aanDU.....2FL5............sD.6....sD0.G.....................
.............oAnAt1...sD....zw1...................................krD3yDR....k1.
.....CnAnz1.......kz/wzzz5EV..6.51...66...E9....m..W4o1.UHU3....8/...6H4....SBDG
Fw4U.qFG9yzb2zzz/Qk7znysV16.pc..zXCc..UAZRBEi7yD6A72QifFjz1............2mwzFrA0.
.Ub96aAIVz9.1se7Umvxz4........../EU0.wzzz1...........s/...................E.2c..
zzzz.............0...................2./8.kzzzD............8....................
/EU0.wzzz1...................................2CcN/UvNPcveeWCNq0.yRiibHJJUk1f..XR
SvBmx3CcN/UvNPcvQsLsUa3.ibhVi1bTV1OK.sSq4uCly3CcN/UvNPcvMwLsUa3.ibhVinqTV1OK.sSq
4uCkz3CcN/UvNPcv..EsUa3feeWCNqGQIJ36wk8EwyLsUa3f................................
E.U..2..F2E.....I....2....UG7FpLbtaOT7JNVl4IjRLNm/pQZJbHZR5Rnw3Am...............
...................6./........0E................................................
................................................................................
........................}
{Titel: NewtTest-Inside}
I have also tried to find a way to either to manipulate bailout conditions (similar as you), or to set x/y/z to values which do diverge when Newton does converge.
However, I assume currently that neither params like Piteration3d^.Rstop can effectively be changed during calculation -
nor any other variables than x, y, and z can simply be taken over from one iteration to the next one.
But well, I was too lazy until now to walk through the M3D source code; and before going to Andreas I would want to make some dedicated tests.
// Note to the community: As this is my first forum entry I'm asking you for your pardon for any mistake I have possibly made.
// Please feel free to tell what I should correct in style, or wording. Thank you!