Logo by dainbramage - Contribute your own Logo!

END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

it was a great time but no longer maintainable by c.Kleinhuis contact him for any data retrieval,
thanks and see you perhaps in 10 years again

this forum will stay online for reference
News: Did you know ? you can use LaTex inside Postings on fractalforums.com!
 
*
Welcome, Guest. Please login or register. March 28, 2024, 06:09:18 PM


Login with username, password and session length


The All New FractalForums is now in Public Beta Testing! Visit FractalForums.org and check it out!


Pages: [1]   Go Down
  Print  
Share this topic on DiggShare this topic on FacebookShare this topic on GoogleShare this topic on RedditShare this topic on StumbleUponShare this topic on Twitter
Author Topic: Burning Bulb  (Read 7139 times)
0 Members and 1 Guest are viewing this topic.
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


WWW
« 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 afro

rendered with pixelbender skript on gpu


* burningbuld.png (855.58 KB, 1113x787 - viewed 1677 times.)

* burningbulb_view1.png (706.86 KB, 1113x787 - viewed 1647 times.)
« Last Edit: December 17, 2009, 08:45:24 PM by Trifox » Logged

---

divide and conquer - iterate and rule - chaos is No random!
kram1032
Fractal Senior
******
Posts: 1863


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

looks way more interesting than the 2D-version cheesy
Logged
matsoljare
Fractal Lover
**
Posts: 215



WWW
« 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...
Logged
bugman
Conqueror
*******
Posts: 122



WWW
« 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: 1863


« 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 wink
Logged
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 1811 times.)

* quaternion-ship-8iterations-zoom.jpg (278.89 KB, 800x600 - viewed 1644 times.)
Logged
bugman
Conqueror
*******
Posts: 122



WWW
« 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 wink

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: 1863


« 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) smiley
Logged
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


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

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

i have corrected the above notation  angel

@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 wink
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

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

---

divide and conquer - iterate and rule - chaos is No random!
BradC
Safarist
******
Posts: 85



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

Do you mean |(x, y, z)| = (|x|, |y|, |z|) ?
Logged
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


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

yes
Logged

---

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
Logged
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
Logged
bugman
Conqueror
*******
Posts: 122



WWW
« 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.
Logged
cKleinhuis
Administrator
Fractal Senior
*******
Posts: 7044


formerly known as 'Trifox'


WWW
« 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 ... wink
Logged

---

divide and conquer - iterate and rule - chaos is No random!
Pages: [1]   Go Down
  Print  
 
Jump to:  

Related Topics
Subject Started by Replies Views Last post
A new class of bulb? Mandelbulb Renderings « 1 2 » cbuchner1 15 5680 Last post December 18, 2009, 02:52:37 PM
by Paolo Bonzini
P 8 bulb inside a P 2 bulb. probably not... Mandelbulb Renderings KRAFTWERK 12 4298 Last post March 08, 2010, 09:45:21 AM
by kram1032
3D burning ship Mandelbulb3D Gallery bib 0 4574 Last post November 02, 2010, 09:34:27 PM
by bib
Burning Fleet 3d Art / Composition tonic 0 1544 Last post March 20, 2011, 01:57:46 PM
by tonic
Inside the Burning Ship Movie bib 0 2933 Last post April 28, 2011, 10:24:17 PM
by bib

Powered by MySQL Powered by PHP Powered by SMF 1.1.21 | SMF © 2015, Simple Machines

Valid XHTML 1.0! Valid CSS! Dilber MC Theme by HarzeM
Page created in 1.148 seconds with 29 queries. (Pretty URLs adds 0.109s, 2q)