Revisiting the 3D Newton

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Offline gforce

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« Reply #15 on: July 25, 2018, 03:31:06 AM »
I have tried another 4D variant (using a 2x2 matrix of real numbers), but the result was too weird.

I would be interested in this variation, I'd be even more interested in that variant with the all the bells and whistles you've added to JIT_gnj_RealPowNewton_04. It might not look good with simple transformations like rotation but i think it will have potential for hybrid formulas :)

Offline FractalDave

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« Reply #16 on: August 09, 2018, 01:03:16 PM »
To produce something really generic one could simply allow the user to define f(h) and g(h) (for 3D h=a+bi+cj) where the "Newton" is performed as:
Code: [Select]
init:
  h = 0 or value from coord for julia
  oldh = 0
  a = value from coord for mandy or constant for julia
loop:
  oldh = h
  h = (f(h) - a) / (g(h) + user const)
Obviously for proper Newtons g(h) should be the derivative of f(h), in particular it should be 1 degree less - but then again why stick to either ?
In this case allowing the option of either divergent or convergent bailout or indeed both might be useful.
The meaning and purpose of life is to give life purpose and meaning.

Offline Sabine62

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« Reply #17 on: August 13, 2018, 09:26:01 AM »
Have tried to port this to Fragmentarium. Has been so long that I have done anything with fractals and still completely lacking any understanding of math, I am so happy that the thing shows anything at all. Have stolen the DE from Mandelbulb, and no optimization at all as will have to read up on that AGAIN after all this time  :fp: :fp: :fp: :embarrass: :embarrass: :embarrass: Neither have any idea what should go into the loop and what not etc etc, it's all just throwing gannjondals newton blindly at fragm, but here it is for your enjoyment (or dispair  :)) )Julia does blow up the whole thing, but added rotations which give really nice results. Also quite some fuzz, so lots  and lots of room for improvement. Oh well...Hope I get some more time to look at it.


Complete .frag in zip below
« Last Edit: August 13, 2018, 09:56:21 AM by Sabine62 »
It's just a jump to the left...

Offline mclarekin

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« Reply #18 on: August 13, 2018, 09:59:15 AM »
looks good.

Thanks for the frag. As usual I have learnt a new thing or two about coding and formulas from looking at it O0

Offline Sabine62

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« Reply #19 on: August 13, 2018, 10:19:39 AM »
Thanks, mclarekin, does look newtonesque, doesn't it ;) Did some minor optimization and updated the frag. Not sure if it will make a big difference though speedwise.


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