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 Author Topic: Burning Bulb  (Read 4214 times) Description: 0 Members and 1 Guest are viewing this topic.
cKleinhuis
Fractal Senior

Posts: 7027

formerly known as 'Trifox'

 « on: December 17, 2009, 03:13:58 AM »

i have entered the rather simple burning ship formula

$z_{n+1}=|z_n|^2+c$

it is the burning buld fractal at 2 exponent ! front and rear view

rendered with pixelbender skript on gpu
 burningbuld.png (855.58 KB, 1113x787 - viewed 701 times.)  burningbulb_view1.png (706.86 KB, 1113x787 - viewed 707 times.) « Last Edit: December 17, 2009, 08:45:24 PM by Trifox » Logged

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divide and conquer - iterate and rule - chaos is No random!
kram1032
Fractal Senior

Posts: 1852

 « Reply #1 on: December 17, 2009, 02:07:04 PM »

looks way more interesting than the 2D-version
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matsoljare
Fractal Lover

Posts: 215

 « Reply #2 on: December 17, 2009, 05:50:26 PM »

The 2D burning ship is very interesting, when you start to zoom in on it...
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bugman
Conqueror

Posts: 122

 « Reply #3 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
 « Last Edit: December 17, 2009, 06:17:09 PM by bugman » Logged
kram1032
Fractal Senior

Posts: 1852

 « Reply #4 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
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gaston3d
Guest
 « Reply #5 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
 quaternion-ship-6iterations.jpg (228.61 KB, 800x600 - viewed 646 times.)  quaternion-ship-8iterations-zoom.jpg (278.89 KB, 800x600 - viewed 678 times.) Logged
bugman
Conqueror

Posts: 122

 « Reply #6 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

If so, then I don't think this is the correct formula for the Burning Ship, but it's still interesting.
 « Last Edit: December 17, 2009, 06:35:34 PM by bugman » Logged
kram1032
Fractal Senior

Posts: 1852

 « Reply #7 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)
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cKleinhuis
Fractal Senior

Posts: 7027

formerly known as 'Trifox'

 « Reply #8 on: December 17, 2009, 08:44:46 PM »

$abs(x)=|x|$ and it is the same for more dimensions sorry for confusion

i have corrected the above notation

@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

 « Last Edit: December 17, 2009, 08:49:54 PM by Trifox » Logged

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divide and conquer - iterate and rule - chaos is No random!
Safarist

Posts: 85

 « Reply #9 on: December 17, 2009, 08:47:32 PM »

Do you mean |(x, y, z)| = (|x|, |y|, |z|) ?
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cKleinhuis
Fractal Senior

Posts: 7027

formerly known as 'Trifox'

 « Reply #10 on: December 17, 2009, 08:50:11 PM »

yes
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divide and conquer - iterate and rule - chaos is No random!
gaston3d
Guest
 « Reply #11 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
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gaston3d
Guest
 « Reply #12 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
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bugman
Conqueror

Posts: 122

 « Reply #13 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.
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cKleinhuis
Fractal Senior

Posts: 7027

formerly known as 'Trifox'

 « Reply #14 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 ...
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divide and conquer - iterate and rule - chaos is No random!
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