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FractalMonster — Not from the Mandelbrot Set by-nc-sa

#exponent #play
Published: 2019-04-15 10:32:14 +0000 UTC; Views: 507; Favourites: 24; Downloads: 12
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Description The tiny little mandy visible in the lower right quadrant in the previous   .
Playing around with the exponent in my compass formula, z -> z^d - da^(d-1) z. See my journal Fractal CompassesNow, my dear readers, I wanna promote the article,
27) Compasses
in my Chaotic series. Along with this journal there are four deviations uploaded,
Compass_d=2
Compass_d=3
Compass_d=4
Compass_d=5

The “d” is the exponent in the iterated polynom p(z) = z^d - da^(d-1) z, the a-plane plotted and “z” initialized to the critical point z = +a. Why this formula is called the “Compass formula”? Well, just look at the above deviations, especially for d = 3 and higher   For d = 3 we actually have z^3 - 3a^2 z whic 
The exponent "d" in this motive is set to EDIT 5+5i.

Software: Ultra Fractal.
Formula: Extended Compasses (adding a parameter "b". the full parameter space becoming a four dimensional hyper space).

Below the UF parametr file. Play and have fun


NotFromTheMandelbrotSet1 {
fractal:
  title="Not from the Mandelbrot Set1" width=800 height=600 layers=1
  credits="Ingvar Kullberg;4/3/2019"
layer:
  caption="Background" opacity=100 method=multipass
mapping:
  center=0.91467894592485/0.61473885163265 magn=1412.657
formula:
  maxiter=10000 percheck=off filename="ik3.ufm"
  entry="ExtendedCompasses" p_exponent=5/5
  p_PlottedPlane="1.(a-real,a-imag)" p_hide=yes p_areal=0.0
  p_aimag=0.0 p_breal=0.0 p_bimag=0.0 p_xrot=0.0 p_yrot=0.0
  p_xrott=0.0 p_yrott=0.0 p_zrot=0.0 p_LocalRot=no p_diff=yes
  p_bailout=10000000 p_dbailout=1E-6
inside:
  transfer=none
outside:
  density=0.5 transfer=linear
gradient:
  smooth=yes rotation=-92 index=26 color=1709847 index=38
  color=16579582 index=47 color=3026462 index=87 color=223 index=105
  color=255 index=-216 color=57075 index=-5 color=16777212
opacity:
  smooth=no index=0 opacity=255
}
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Comments: 9

Pen-and-mouse [2019-04-20 09:03:22 +0000 UTC]

This is so not right it makes my head hurt in a way! But I like that!

👍: 0 ⏩: 1

FractalMonster In reply to Pen-and-mouse [2019-04-20 10:16:52 +0000 UTC]

Check out my short journal The Universality of Little MandysIn many of my recent uploads, little mandys are often seen, sometimes little distorted. This is quite natural in motives that are zoomed in from the ordinary Mandelbrot set, as the branches, which are connected, are entirely build up of mini copies of the Mandelbrot set. However most of the images, so far posted by me, these mini copies are NOT parts of the Mandelbrot set. They come from cubic formulas, compass formulas, Quartics, and soon Pentics. They can also be found in Newton formulas, trigonometric fucntions etc. This is a very fascinating thing. Whenever a function is iterated in such a way that the variable is initiated to a so called "critical point" and a parameter plane is plotted, there is a very good chance that copies of the Mandelbrot set (little mandys) can be found.
So the Mandelbrot set, generated by the simplest non linear function that can be iterated, the quadratic formula, z -> z^2 + c, the variable z initiated to the critical point z = 0, the parameter c = #pi 

👍: 0 ⏩: 1

Pen-and-mouse In reply to FractalMonster [2019-04-23 08:56:12 +0000 UTC]

I will!

👍: 0 ⏩: 1

FractalMonster In reply to Pen-and-mouse [2019-04-23 09:51:13 +0000 UTC]

Yo apparently DID

👍: 0 ⏩: 0

Leanndra51 [2019-04-15 16:17:11 +0000 UTC]

Gotta love that beautiful RED surrounding that wonderful bright yellow!  I really love this. 

👍: 0 ⏩: 2

Psychedelic-Factory In reply to Leanndra51 [2019-04-17 11:02:02 +0000 UTC]

Truly AMAZING 

👍: 0 ⏩: 1

FractalMonster In reply to Psychedelic-Factory [2019-04-17 16:53:21 +0000 UTC]

Really glad you like it


More will come

👍: 0 ⏩: 0

FractalMonster In reply to Leanndra51 [2019-04-15 17:44:54 +0000 UTC]

That's my favorite type of coloring More of this kind will be uploaded


.. and thanks for the

👍: 0 ⏩: 1

Leanndra51 In reply to FractalMonster [2019-04-15 19:21:13 +0000 UTC]

Awesome!

👍: 0 ⏩: 0