• May 18, 2021, 03:46:58 PM

### Author Topic:  Terra Newtonia  (Read 1458 times)

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#### gannjondal

• Fractal Phenom
• Posts: 47
##### Terra Newtonia
« on: January 02, 2021, 09:18:19 PM »
Working on my Newton method formulas for Mandelbulber, and Fragmentarium brought me back to the addiction to explore that class of formulas.
Used pure this type of formula is mostly boring.
But they are good for hybridisation, mutation etc.
To stop spamming the theory borads, and to provide an overview (also for myself) I decided to start an image thread with completely unsorted pictures related to the Newton-Raphson method.

For completeness my other related threads:
https://fractalforums.org/fractal-mathematics-and-new-theories/28/revisiting-the-3d-newton/1026
https://fractalforums.org/fractal-mathematics-and-new-theories/28/slightly-extended-newton-method-fractals/3067

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #1 on: January 02, 2021, 09:20:47 PM »
My first set of images.

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtCS_3/4.m3f (pure, just combinations of that formula with different values)
Params, and formulas are attached (m3d1-1731_1736.zip).

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #2 on: January 02, 2021, 09:24:43 PM »
And a second entry for today.

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtCS_1.m3f (plus a  _Translate)
Params, and formulas are attached (m3d1-1725.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #3 on: January 06, 2021, 08:06:21 PM »
... and three new pictures.

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewt_v1_01.m3f (plus _RotatedFolding, and partially _Transform)
Params, and formulas are attached (m3d1-1732_35-v199-34_paramsFormulas.zip)

#### hobold

• Fractal Frogurt
• Posts: 434
##### Re: Terra Newtonia
« Reply #4 on: January 07, 2021, 01:20:28 AM »
I really should have voiced some appreciation earlier. These all strike me as unconventional, somewhat fresh and different from existing crops of 3D fractals. And yet they do have some family resemblance.

I cannot say if this is caused by the Newton formula or by your artistic handwriting. But I like that you opened a window to a notably different set of interesting vistas. Thanks!

#### mclarekin

• 3c
• Posts: 856
##### Re: Terra Newtonia
« Reply #5 on: January 07, 2021, 01:37:19 AM »
looking good with the rotated folding.

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #6 on: January 10, 2021, 06:21:31 PM »
@hobold , and @mclarekin - Thank you very much for your kind comments

Regarding the mentioned "family resemblance":
I find that the formula family generates quite varied kinds of pictures.
But maybe that's just my impression since I have done too much with those formulas

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #7 on: January 10, 2021, 06:25:28 PM »
This time I have played around with a lengthy list of transformations:

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtonS_2 - _Translate - _Rotate - _Translate - _RotatedFolding
Params, and formulas are attached (m3d1-1721a-008-v199-34.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #8 on: January 14, 2021, 08:19:28 PM »
Newton formulas are also good as pre-transformations.
More to come....

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtonS_2 (2 iterations)  ->  Integer Power
Params, and formulas are attached (m3d1-1536-01.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #9 on: January 18, 2021, 06:01:05 PM »
Two pictures of my more recent findings...

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtCS_3.m3f
Params, and formulas are attached (m3d1-1729-057-83.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #10 on: January 21, 2021, 09:29:12 PM »
These two use the same combination of formulas....

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtCS_1 - _Translate - JIT_gnj_RealPowNewtCS_1
Params, and formulas are attached (m3d1-1725-044+033.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #11 on: February 04, 2021, 09:54:32 PM »
And a new one - this time very simple...

Program used:  Mandelbulb3D v199-34
Formulas:  2x JIT_gnj_RealPowNewtCS_1 with different parameters
Params, and formulas are attached (m3d1-1723k-004a.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #12 on: February 10, 2021, 10:12:31 PM »
Today some rays...

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtonS_1, and MengerIFS
Params, and formulas are attached (m3d1-1281-data.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #13 on: February 18, 2021, 09:54:01 PM »
Of course the birdies cannot be missing.
I think these two have not been published yet.

Program used:  Mandelbulb3D v199-34
Formulas:  JIT_gnj_RealPowNewtBoxS03, _RotatedFolding, _Rotate
Params, and formulas are attached (m3d1-1464-1464.zip)

#### gannjondal

• Fractal Phenom
• Posts: 47
##### Re: Terra Newtonia
« Reply #14 on: March 04, 2021, 08:53:25 PM »
Today some nice cut with one of the most simple 3D Newton formulas...

Program used:  Mandelbulb3D v199
Formulas:  Tricorn, JIT_gnj_Pow3Newton_01
Params, and formulas are attached (m3d1-1237-019-params.zip)

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