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#compass #exponent #formula #playing
Published: 2019-04-24 17:21:43 +0000 UTC; Views: 539; Favourites: 23; Downloads: 6
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This one is a zoom-in into the tiny black dot visible in the upper left in the earlier deviationPlaying 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
The exponent "d" in this motive is set to 0+2i.
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
NotFromTheMandelbrotSet4 {
fractal:
title="Not from the Mandelbrot Set4" width=800 height=600 layers=1
credits="Ingvar Kullberg;4/13/2019"
layer:
caption="Background" opacity=100 method=multipass
mapping:
center=1.2617592572061/0.038907629385318 magn=4120.034
formula:
maxiter=10000 percheck=off filename="ik3.ufm"
entry="ExtendedCompasses" p_exponent=0/2
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-10
inside:
transfer=none
outside:
density=0.1 transfer=linear
gradient:
smooth=yes rotation=-111 index=7 color=1709847 index=19
color=16579582 index=28 color=3026462 index=68 color=223 index=86
color=255 index=-235 color=57075 index=-24 color=16777212
opacity:
smooth=no index=0 opacity=255
}
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Comments: 9
FractalRock [2019-07-14 02:17:35 +0000 UTC]
The web of gray around the red-outlined mandelbrot looks exceptional. Great job!
👍: 0 ⏩: 1
FractalMonster In reply to FractalRock [2019-07-14 10:24:32 +0000 UTC]
It IS! Those broken structures are the result of the variable's
exponent not being a real number of 2 or greater ..
.. and thanks for the s
👍: 0 ⏩: 0
FractalMonster In reply to sed [2019-04-29 08:44:30 +0000 UTC]
No problem
BTW, see you are a talent fractal artist Maybe you would appreciate my Chaotic series of fractal articles (<- click) if you have a little theoretical interest
👍: 0 ⏩: 1
Leanndra51 [2019-04-24 21:39:21 +0000 UTC]
A real beauty here too! Love all that silvery look!
👍: 0 ⏩: 1
FractalMonster In reply to Leanndra51 [2019-04-24 21:56:29 +0000 UTC]
Maybe a little bit repetition of the previous ones
👍: 0 ⏩: 0