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FractalMonster — Flow of Life by-nc-sa

#cubic #parameterspace
Published: 2018-08-20 21:01:20 +0000 UTC; Views: 247; Favourites: 24; Downloads: 3
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Description An in-zoom into my previous deviation which is a magnification in a 2D-slice of the four dimensional cubic parameter space using the standard parameterizing z -> z^3 - 3a^2 z + b, critical points z = +a and z = -a
 
*a_real = 0.15
*a_imag = #pixel (horizontal)
*b_real = 0.15
*b_imag = #pixel (vertical)
 
Both M+ and M- are displayed, each in separate layer.
 
No filters or postprocessing except anti-aliasing (from 6400 x 4800).
 
Ultra Fractal, formula Cubic Parameterspace3 in the sp3-module written by my dear friend Greenseng here on DeviantART. All his modules, as well as mine can be downloaded from here (right click).
 
Below the parameter file. Play and have fun
 
 
FlowOfLife {
fractal:
  title="Flow of Life" width=800 height=600 layers=2
  credits="Ingvar Kullberg;8/18/2018"
layer:
  caption="M-" opacity=100 mergemode=green method=multipass
mapping:
  center=-0.48100914188247275/0.7040775306196721 magn=2701892
formula:
  maxiter=1000000 filename="sp3.ufm" entry="CubicParameterspace3"
  p_PlottedPlane="5.(a-imag,b-imag)" p_M=M- p_SetBorders=no p_hide=yes
  p_areal=0.15 p_aimag=0.0 p_breal=0.15 p_bimag=0.0 p_xrot=0 p_yrot=0
  p_xrott=0 p_yrott=0 p_zrot=0 p_LocalRot=no p_diff=no p_bailout=100
  p_dbailout=1E-6
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=4 index=191 color=13331226 index=328
  color=16711663 index=353 color=38143 index=360 color=3474452
  index=-34 color=11665408
opacity:
  smooth=no index=0 opacity=255
layer:
  caption="M+" opacity=100 method=multipass
mapping:
  center=-0.48100914188247275/0.7040775306196721 magn=2701892
formula:
  maxiter=1000000 filename="sp3.ufm" entry="CubicParameterspace3"
  p_PlottedPlane="5.(a-imag,b-imag)" p_M=M+ p_SetBorders=no p_hide=yes
  p_areal=0.15 p_aimag=0.0 p_breal=0.15 p_bimag=0.0 p_xrot=0 p_yrot=0
  p_xrott=0 p_yrott=0 p_zrot=0 p_LocalRot=no p_diff=no p_bailout=100
  p_dbailout=1E-6
inside:
  transfer=none
outside:
  transfer=linear
gradient:
  smooth=yes rotation=-141 index=46 color=2445567 index=-132
  color=327680 index=-101 color=15794175 index=-89 color=655360
  index=-34 color=16769274
opacity:
  smooth=no index=0 opacity=255
}
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Comments: 11

teddybearcholla [2018-09-07 02:43:20 +0000 UTC]

👍: 0 ⏩: 1

FractalMonster In reply to teddybearcholla [2018-09-07 09:24:25 +0000 UTC]


..and thanks Barb for the s

👍: 0 ⏩: 1

teddybearcholla In reply to FractalMonster [2018-09-08 20:32:08 +0000 UTC]

 

👍: 0 ⏩: 1

FractalMonster In reply to teddybearcholla [2018-09-08 20:41:35 +0000 UTC]

👍: 0 ⏩: 1

teddybearcholla In reply to FractalMonster [2018-09-08 20:43:08 +0000 UTC]

👍: 0 ⏩: 0

Leanndra51 [2018-08-20 22:35:31 +0000 UTC]

Continuing on in that same vein of thought from the other image I commented on, when I read that this is from, "a 2D-slice of the four dimensional cubic parameter space", just thinking about that boggles my little brain!   

👍: 0 ⏩: 1

FractalMonster In reply to Leanndra51 [2018-08-20 23:10:25 +0000 UTC]

Two parameters (a and b), which are complex thus having 2 axis each, makes 4 axis'


BTW, thanks for the s

👍: 0 ⏩: 1

Leanndra51 In reply to FractalMonster [2018-08-21 00:26:18 +0000 UTC]

That is the part that I actually got!    I barely passed Algebra in 9th grade, and never took any higher math classes, no geometry.  But after all these years when I read that part the other day, it was clear to me what was meant.  Pretty neat for someone who never got it!  At this rate by the time I am 105, I will have it figured out!   

You are welcome, my friend!

👍: 0 ⏩: 1

FractalMonster In reply to Leanndra51 [2018-08-21 10:21:12 +0000 UTC]

Nobody can imagine more than 3 spatial dimension. that's the problem. Handle more dimensions requires to go beyond our imagination(s)

👍: 0 ⏩: 1

Leanndra51 In reply to FractalMonster [2018-08-22 06:16:25 +0000 UTC]

I know!  Have read this book and loved it! 

en.wikipedia.org/wiki/Flatland

👍: 0 ⏩: 1

FractalMonster In reply to Leanndra51 [2018-08-22 09:53:38 +0000 UTC]

That's a funny story I've come into touch with earlier


Thanks for pointing it out

👍: 0 ⏩: 0