Title: Burning Bulb
Post by: cKleinhuis on December 17, 2009, 03:13:58 AM
i have entered the rather simple burning ship formula
it is the burning buld fractal at 2 exponent ! front and rear view O0
rendered with pixelbender skript on gpu
it is the burning buld fractal at 2 exponent ! front and rear view O0
rendered with pixelbender skript on gpu
Title: Re: Burning Bulb
Post by: kram1032 on December 17, 2009, 02:07:04 PM
looks way more interesting than the 2D-version :D
Title: Re: Burning Bulb
Post by: matsoljare on December 17, 2009, 05:50:26 PM
The 2D burning ship is very interesting, when you start to zoom in on it...
Title: Re: Burning Bulb
Post by: bugman on December 17, 2009, 06:14:17 PM
Very neat! I'm not clear what do you mean by abs(z)? For the complex case it should be: xnew+iynew = x²-y² + 2i|xy| - zc
Title: Re: Burning Bulb
Post by: kram1032 on December 17, 2009, 06:15:33 PM
abs z is clear.
it's just the radius with phi=0° and theta=0°
just compare polar coordinate complex abs ;)
it's just the radius with phi=0° and theta=0°
just compare polar coordinate complex abs ;)
Title: Re: Burning Bulb
Post by: gaston3d on December 17, 2009, 06:17:18 PM
what algebra is it?
i've got different results with quaternions:
z[n+1] = (abs(z.a) + abs(z.b)*i + abs(z.c)*j + abs(z.d)*k)^2 + h
Title: Re: Burning Bulb
Post by: bugman on December 17, 2009, 06:19:50 PM
abs z is clear.
it's just the radius with phi=0° and theta=0°
just compare polar coordinate complex abs ;)
it's just the radius with phi=0° and theta=0°
just compare polar coordinate complex abs ;)
If so, then I don't think this is the correct formula for the Burning Ship, but it's still interesting.
Title: Re: Burning Bulb
Post by: kram1032 on December 17, 2009, 06:46:08 PM
ah, wait, yeah, forgot...
abs(real)+abs(imag) for complex...
well...
convert from spherical to cartesian and then
abs(x) abs(y) abs(z) :)
abs(real)+abs(imag) for complex...
well...
convert from spherical to cartesian and then
abs(x) abs(y) abs(z) :)
Title: Re: Burning Bulb
Post by: cKleinhuis on December 17, 2009, 08:44:46 PM
i have corrected the above notation :angel1:
@gaston3d the used algebra is polar coordinate triplex, d.white & p.nylanders version, as defined on:
http://www.fractalforums.com/theory/triplex-algebra/
i will go and try to find more simple base fractals, was experimenting with barnsley. until i understand how to modify the derivations for new functions i will wait for trying newtonian, or diverging fractals ;)
it is very enjoying seeing that thing morph in realtime on my gts250 gpu, i really hope there will be a numbers library with arbitrary precision for gpus soon to work with greater precision
:evil1:
Title: Re: Burning Bulb
Post by: BradC on December 17, 2009, 08:47:32 PM
Do you mean |(x, y, z)| = (|x|, |y|, |z|) ?
Title: Re: Burning Bulb
Post by: cKleinhuis on December 17, 2009, 08:50:11 PM
yes
Title: Re: Burning Bulb
Post by: gaston3d on December 17, 2009, 09:10:16 PM
i think formula z[n+1] = |z[n]|^2 + c is still improper and is equivalent to z[n+1] = z[n]^2 + c
one of definitions of absolute value is: abs(a+bi+...) = sqrt(a^2+b^2+...), then (abs(z))^2 = z^2
Title: Re: Burning Bulb
Post by: gaston3d on December 17, 2009, 09:28:42 PM
... i really hope there will be a numbers library with arbitrary precision for gpus soon to work with greater precision ...
i am not into gpu programing, but read somewhere that 64 bit double precision were introduced in shader model 5 (directx11) and is supported by nvidia gt200 chipset
Title: Re: Burning Bulb
Post by: bugman on December 17, 2009, 09:48:56 PM
Do you mean |(x, y, z)| = (|x|, |y|, |z|) ?
You might also want to try {|x|, |y|, z}, as that seems to give interesting results as well, and the cross section in the x-y plane still contains the 2D Burning Ship fractal.
Title: Re: Burning Bulb
Post by: cKleinhuis on December 17, 2009, 10:15:07 PM
Do you mean |(x, y, z)| = (|x|, |y|, |z|) ?
You might also want to try {|x|, |y|, z}, as that seems to give interesting results as well, and the cross section in the x-y plane still contains the 2D Burning Ship fractal.
yes, that is what i did, i think it is nice to have possible 3d analogons of existing fractals using the triplex algebra, i am right now into trying several formulas, which do not need
additional functions ( sin,cos ... )
btw. having the original 2d complex numbers fractal in one plane is a must ... ;)