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 Author Topic: Another true 3D fail ?  (Read 1517 times) Description: 0 Members and 1 Guest are viewing this topic.
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « on: December 16, 2012, 05:43:05 AM »

This one's pretty interesting with or without the scale of the power 5 by  (1.0-abs(real(z))/m)...

Code:

m = sqrt(|z|+sqr(real(w)))
if m>0.0
complex t = (1.0-abs(real(z))/m)*(imag(z)+flip(real(w)))^5.0 + flip(2.0*real(z)*real(w))
z = sqr(z)-sqr(real(w))+flip(real(t))
w = imag(t)
endif
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
DarkBeam
Global Moderator
Fractal Senior

Posts: 2512

Fragments of the fractal -like the tip of it

 « Reply #1 on: December 16, 2012, 09:53:56 AM »

Everybody want an image David
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No sweat, guardian of wisdom!
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « Reply #2 on: December 16, 2012, 10:52:31 AM »

Everybody want an image David

I don't wanna spoil the surprise
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The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
M Benesi
Fractal Schemer

Posts: 1075

 « Reply #3 on: December 17, 2012, 03:52:12 AM »

Code:

m = sqrt(|z|+sqr(real(w)))
if m>0.0
complex t = (1.0-abs(real(z))/m)*(imag(z)+flip(real(w)))^5.0 + flip(2.0*real(z)*real(w))
z = sqr(z)-sqr(real(w))+flip(real(t))
w = imag(t)
endif

Is w complex?  Assigning w=imag(t) tends to make me think it isn't- it should only have a real component then.

Looks like:
m=...
if  m!=0 {
t= (1-abs(x))/m) * (y+z)^5 + i * 2xz;
k= k^2 - z^2  +  i * real (t) ;

w= imag(t)
}

What is it, a "squarey" brot?

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David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « Reply #4 on: December 17, 2012, 04:32:04 AM »

Is w complex?  Assigning w=imag(t) tends to make me think it isn't- it should only have a real component then.

Looks like:
m=...
if  m!=0 {
t= (1-abs(x))/m) * (y+z)^5 + i * 2xz;
k= k^2 - z^2  +  i * real (t) ;

w= imag(t)
}

What is it, a "squarey" brot?

No all vars are complex but outside the calculation the imaginary part of w remains zero. It's basically standard quaternion cut down to 3D (i.e. (x,y,z)) but with (y+flip(z))^5 added to the y and z terms - if this part is scaled by (1.0-abs(x)/m) then the x+y and x+z plane slices are both the standard complex Mandy and the y+z plane is the complex degree 5 Mandy i.e. with 4 bulbs around the main.

Here it is anyway...a fail, but a damn interesting one

www.fractalforums.com/index.php?action=gallery;sa=view;id=12983

 « Last Edit: December 17, 2012, 04:34:44 AM by David Makin » Logged

The meaning and purpose of life is to give life purpose and meaning.

http://www.fractalgallery.co.uk/
"Makin' Magic Music" on Jango
M Benesi
Fractal Schemer

Posts: 1075

 « Reply #5 on: December 17, 2012, 05:55:27 AM »

Definitely cool.

I still find that taking the "xmas tree" formula (semi Julia mode- full xyz seed, followed by addition of ONLY x-axis component *.5), rotating the x-axis to the magnitude axis (-1,-1,-1) to (1,1,1),

applying the following transform:

x= 2.*abs(x) -1.
y=2.*abs(y) -1.
z=2.*abs(z)-1.

followed by a rotation back to the x axis makes the fractallyest z^2s...
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jehovajah
Global Moderator
Fractal Senior

Posts: 2749

May a trochoid in the void bring you peace

 « Reply #6 on: January 08, 2013, 12:36:46 PM »

The sophistication of these images is amazing!
Davids so called fail compared with what was achieved early in he holy grail hunt really shows how far we have come in tinkering. Matt's solution shows how far we can go towards different design goals.
Great works, guys!
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May a trochoid of ¥h¶h iteratively entrain your Logos Response transforming into iridescent fractals of orgasmic delight and joy, with kindness, peace and gratitude at all scales within your experience. I beg of you to enrich others as you have been enriched, in vorticose pulsations of extravagance!
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