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Author Topic: newton 3d+ new formula and picture  (Read 1684 times)
Description: test for a 3d newton
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ericr
Fractal Fanatic
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Posts: 318


« on: January 10, 2016, 04:30:18 PM »

test for a 3d newton
I waiting the critiques , I m not sure to have done a real newton fractal (I only hope so)

(c+sin(x))/cos(x))- x

on deviant art a wonderfull newton 3d has be done , I try do the same but it is very very hard !!!!!!
(if your alone)

* JIT_newton.m3f (1.15 KB - downloaded 76 times.)

* newton sin.jpg (102 KB, 480x360 - viewed 583 times.)
« Last Edit: January 18, 2016, 03:17:31 PM by ericr » Logged
JosLeys
Strange Attractor
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Posts: 258


WWW
« Reply #1 on: January 16, 2016, 08:54:07 AM »

Your formula is not for the Newton fractal.
Look here first:  https://en.wikipedia.org/wiki/Newton_fractal

Here is a page of 3D Newton fractals done in Ultrafractal: http://www.josleys.com/show_gallery.php?galid=338
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ericr
Fractal Fanatic
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Posts: 318


« Reply #2 on: January 16, 2016, 12:54:33 PM »

sorry, yes the formula was worng !
It's z-c*f(z)/f'(z)  but in 3d i must do x':=x*cos(a)sin(b)
                                                        y':=y*cos(a)cos(b)
                                                        z':=z*sin(a)
and x=x-c*f(x)/f'(x) y and z the same

I make a new jit formual but it s not the god fractal result huh??

* JIT_newton.m3f (1.27 KB - downloaded 79 times.)
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ericr
Fractal Fanatic
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Posts: 318


« Reply #3 on: January 17, 2016, 04:27:11 PM »

my last version of newton 3d
after help of jesleys but the result is not ok

no:=sqrt(((x1-x)*(x1-x))+((y1-y)*(y1-y))+((z1-z)*(z1-z)));
             ed:=-k*((1-exp(-m*no))/(1+exp(-m*no)));
             Piteration3d^.Rstop:=ed;

this parte calcul the DE using -k*(1-exp(-mED))/(1+exp(-mED))




* JIT_newton.m3f (1.18 KB - downloaded 73 times.)

* newton3d 11.jpg (96.4 KB, 500x375 - viewed 328 times.)
« Last Edit: January 18, 2016, 03:10:54 PM by ericr » Logged
gannjondal
Forums Freshman
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Posts: 17


« Reply #4 on: March 01, 2016, 11:38:15 PM »


Better later than never, Eric smiley -
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  evil).
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:
Code:
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:
Code:
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:
Code:
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!

* JIT_gnj_RealPowerPseuNewt3_02.m3f (1.88 KB - downloaded 78 times.)
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hobold
Fractal Bachius
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Posts: 573


« Reply #5 on: March 02, 2016, 09:49:55 AM »

Don't worry, gannjondal, your post is informative and illustrated very well. That would be a good standard even for a 1000th posting. smiley
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ericr
Fractal Fanatic
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Posts: 318


« Reply #6 on: March 02, 2016, 10:05:15 AM »

Thx very much and thx for all formulas and deviantart
Eric
« Last Edit: March 02, 2016, 11:32:02 AM by ericr » Logged
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