Welcome to Fractal Forums

upon user request:
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/glowing-cube-divided/msg77019/#msg77019

i created a visualisation of the burning ship iteration,
if you have any special wish what i shall visualise let me know

enjoy:
https://www.youtube.com/watch?v=oJjjoCe5MY0

"This video is private", am I just too quick at only 6 minutes after your post?

now it is public, i had to press some buttons and confirm my identity, enjoy! music by chillheimer!

I guess stardust requested this after I asked a question about this.

Very usefull!

it was youhn that pointed it ;) here:
http://www.fractalforums.com/images-showcase-(rate-my-fractal)/glowing-cube-divided/msg77019/#msg77019

Very Nice video!

Speaking of the Burning Ship, I don't know if you have already explored the other two (made by not folding all variables)..
replacing the ship abs function (in fractint and ultrafractal formats):

z=abs(real(z))+flip(abs(imag(z)))

by

z=abs(real(z))-flip(imag(z))

or by

z=real(z)+flip(-abs(imag(z)))

They both create very interesting sets to explore (in special in the mirror spiral department)..
Also, try the Quadray Burning ship, using the abs on the Quadray set.. I call that one, the Burning Fish because ilooks like that.
There's another, but in the Nova formula (the newton iteration).. but that's another history..  ;D

ok, i might visualise them as spin offs, folding justx and justx, will check it ;)

Just don't forget the signs!
z=abs(real(z))-flip((imag(z)))
and
z=abs(real(z))+flip((imag(z)))
are not the same! ;D
(The Julias are interesting in both cases!, but one the sets isn't)

yay, i saw it, the "+" does not look very interesting, although it is fractal

i am thinking how to incorporate it in the tutorial, perhaps i include them as spin offs, for the negative multiplication by1 i need to adjust my visuals because it is a rotation around the x axis and not a fold ;) although it could be visualised as fold it would look weird to fold opposite side against eachother

though, i wonder why the heck arent they the same? the abs should render the negation obsolete :( ???

woah, the julias are quite cool, this is the julia

z=abs(real(z))+flip((imag(z)))
z=z^2+c

BUT, for the julia i am preparing a special issue explaining the difference julia/mandelbrot method, which makes crystal clear why the mandelbrot pops out, you might have recognised the mandelbrot tutorial is not finished and it started from back (4.4) in issue 4.3 i want to point out the difference (different starting location, same addition for every point, mandelbrot set is a map of julias that are connected ;) )

-abs(x) and abs(x) aren't the same!  ;D

Actually I consider these sets some sort of halfway between both the Burning Ship and the Mandelbrot set because they share the properties of both..
The Julias reflects this property very well (in special of the julias of the spiral kind)
Here are two images, one little zoomed area of one of the mandelbrot and a julia set.


Oh.. the relationship between the Mandebrot and Julia becomes complicated when you use perturbations (different starting points)..
They are often overlooked, but they can generate very interesting images if you use them in a dynamic way.. :)

right, but in both formulas the abs is outside, abs(x) and abs(-x) should be the same ...

Hmm.. no.. look again (Fractint format can be a little tricky):
z=abs(real(z))-flip(imag(z))
and
z=real(z)+flip(-abs(imag(z)))

In a more formal way:
z=Complex( abs(zr), -zi )
and
z=Complex( zr, -abs(zi) )

 :)

There it is. Many thanks Christian!   :D

Funny how the most interesting quadrant is the one where all the points get folded out of. The translation is again beautiful to watch! A suprise is the resulting smoothness of the inner structures. I see more curved lines than sharp folds, so it might approach analytical math in some properties.

i see, fold direction is just inverted i am going to visualise the most interesting ones, playing just with the folds gives good insights

in fact it turned out quite informative, using only abs(z.imaginary) and -abs(z.imaginary) yields the same result just flipped, visualisations are rendering right now and will be published tomorrow, it gives fantastic insight to the mirroring of complex numbers, although the multiplication seems quite different the result is the same, just flipped!