### Playing with 4D types.....

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#### Playing with 4D types.....

« on: August 09, 2018, 10:33:25 AM »
Just revisited some old test formulas I tried, this probably produces the most interesting results.
See examples (rendered in Ultra Fractal).
The formula for (z,w)^2 where z and w are both complex is:

Code: [Select]
      s = |z|      t = |w| ; i.e. mag(z)^2 and mag(w)^2      if s+t>0        if s>=t          w = 2.0*z*w          z = sqr(z)*(1.0 - t/s)        else          wt = w          w = 2.0*z*w          z = (s/t-1.0)*sqr(wt)        endif      endif

Linkback: https://fractalforums.org/fractal-mathematics-and-new-theories/28/playing-with-4d-types/1713/
« Last Edit: August 09, 2018, 12:30:22 PM by FractalDave »
The meaning and purpose of life is to give life purpose and meaning.

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#### Re: Playing with 4D types.....

« Reply #1 on: August 09, 2018, 12:39:39 PM »
Just to add that "Motie" in the title of the first example image comes from the sci-fi book "The Mote in God's Eye" - the Moties were asymmetric aliens on a planet with a high background radiation count.

#### Kalter Rauch

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#### Re: Playing with 4D types.....

« Reply #2 on: August 13, 2018, 07:15:09 PM »
FractalDave...Thanx for the info.
In addition to UF formulas
there are also some Makin4D formulas in M3D
which I'm now experimenting on...

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#### Re: Playing with 4D types.....

« Reply #3 on: August 14, 2018, 03:38:22 AM »
I know, I have an oldish Mac version of M3D though I haven't tried it much yet. The 4D iteration formula I posted here is not one of those already in there, it's just one I was trying myself. I'm currently working on tidying up my Wip3D formula for UF to the point where I'm happy to release it to the actual UF formula database, including adding an easier way for folks to add their own 3D/4D formula options (iteration calculations including those for running sums for analytical distance estimation if they wish).

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