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 Author Topic: LambdaBulb  (Read 10038 times) Description: 0 Members and 1 Guest are viewing this topic.
fractalrebel
Fractal Lover

Posts: 211

 « on: November 23, 2009, 11:53:19 PM »

Here is a bit different type of beast. Its a 4th power lambdabulb with a seed of 1.0625 + i*0.2375 with shadows. The function is $z = c*(z-z^p)$. The first image shows the lambdabulb viewed from the top (along the z axis) and the second is from the side (along the y axis).
 LambdaBulb_4th_front.jpg (96.56 KB, 640x640 - viewed 2476 times.)  LambdaBulb_4th_side.jpg (67.42 KB, 640x640 - viewed 2422 times.) Logged

cKleinhuis
Fractal Senior

Posts: 7044

formerly known as 'Trifox'

 « Reply #1 on: November 24, 2009, 12:10:59 AM »

oh yeah, this is what i call a nice object !
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---

divide and conquer - iterate and rule - chaos is No random!
David Makin
Global Moderator
Fractal Senior

Posts: 2286

 « Reply #2 on: November 24, 2009, 12:45:24 AM »

Nice one Ron !
I have an idea for doing a pseudo-Newton
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The meaning and purpose of life is to give life purpose and meaning.

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fractalrebel
Fractal Lover

Posts: 211

 « Reply #3 on: November 24, 2009, 05:40:42 AM »

Here is a fractal version of a Segway. This is a lambdabulb that is the standard power of two. The julia seed is 0.964 - i*0.303.
 Segway.jpg (45.98 KB, 640x512 - viewed 2363 times.) Logged

JColyer
Guest
 « Reply #4 on: November 24, 2009, 07:59:51 PM »

Ohhh pretty...  hmmm... have to slice these things open and see what makes 'em tick!
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JColyer
Guest
 « Reply #5 on: November 25, 2009, 12:58:50 AM »

@fractalrebel - mind sharing your expansion (code) for the lambda bulb formula?  I'm trying to get it right, but something's really wrong with the pictures I'm generating!!

I tried adapting the 'standard' 3d mandelbulb code, but seems like I'm missing something.....

Thanks!

JC
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fractalrebel
Fractal Lover

Posts: 211

 « Reply #6 on: November 25, 2009, 04:22:23 AM »

@fractalrebel - mind sharing your expansion (code) for the lambda bulb formula?  I'm trying to get it right, but something's really wrong with the pictures I'm generating!!

I tried adapting the 'standard' 3d mandelbulb code, but seems like I'm missing something.....

Thanks!

JC

All of my code object oriented Ultrafractal 5 code. I define a function for taking powers in spherical coordinates, and an other for multiplication. The target function is $z=c(z-z^p)$ where c is the 3D complex number for the Julia seed. Here is the power function. the vectors are 4D vectors. a is the input vector and b is the output vector. The vectors are a convenient target for the mapping to two complex numbers. Obviously the 4th dimension component is always zero (at least for bulb fractals).

static func Spower(bool altel, float power, Vector a, Vector b)
; Power function for s = x + iy + jz expressed in spherical coordinates
float r = sqrt(a.m_x^2 + a.m_y^2 + a.m_z^2)+1e-10
float phi = atan2(a.m_x + flip(a.m_y))  ; azimuth
float theta = 0
if altel
theta = asin(-a.m_z/r)
else
theta = asin(a.m_z/r)
endif
r = r^power
phi = power*phi
theta = power*theta
b.m_x = r*cos(theta)*cos(phi)
b.m_y = r*cos(theta)*sin(phi)
b.m_z = r*sin(theta)
b.m_w = 0
endfunc

Here is rhe multiplication function. a and b are the two input vectors and c is the output vector.

static func SMult(bool altel, Vector a, Vector b, Vector c)
float ra = sqrt(a.m_x^2 + a.m_y^2 + a.m_z^2)+1e-10
float phia = atan2(a.m_x + flip(a.m_y))  ; azimuth
float thetaa = 0
if altel
thetaa = asin(-a.m_z/ra)
else
thetaa = asin(a.m_z/ra)
endif
float rb = sqrt(b.m_x^2 + b.m_y^2 + b.m_z^2)+1e-10
float phib = atan2(b.m_x + flip(b.m_y))  ; azimuth
float thetab = 0
if altel
thetab = asin(-b.m_z/rb)
else
thetab = asin(b.m_z/rb)
endif
float r = ra*rb
float phi = phia + phib
float theta = thetaa + thetab
c.m_x = r*cos(theta)*cos(phi)
c.m_y = r*cos(theta)*sin(phi)
c.m_z = r*sin(theta)
c.m_w = 0
endfunc
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JColyer
Guest
 « Reply #7 on: November 25, 2009, 01:52:24 PM »

ron - thanks for the code mine was really close but I had the multiply function implemented as a standard vector cross product and that was screwing me up.  should have an image posted later today.
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fractalrebel
Fractal Lover

Posts: 211

 « Reply #8 on: November 27, 2009, 09:08:35 PM »

The following image is an 8th power lambdabulb with a seed of 0.046411130776+ i*1.2609375008. There appears to be a gryphon on a throne hiding in the fractal.
 GryphonGuardianOfLambda640_512.jpg (107.49 KB, 640x512 - viewed 2264 times.) Logged

bugman
Conqueror

Posts: 122

 « Reply #9 on: December 01, 2009, 07:13:21 AM »

Ron, I really like your rendering of the Lamdabulb at the top of this post. I'd like to see more unusal formulas like this. Here are some of my renderings of it. The lower image is with a negative sign (using your notation altel = true).
 Lambdabulb.jpg (116.86 KB, 563x282 - viewed 2268 times.)  Lambdabulb-.jpg (61.99 KB, 280x280 - viewed 2322 times.) Logged
kram1032
Fractal Senior

Posts: 1863

 « Reply #10 on: December 02, 2009, 01:00:44 AM »

also a great variant
I really like them a lot!
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miner49er
Safarist

Posts: 82

 « Reply #11 on: December 02, 2009, 09:53:45 PM »

That one in the lower left looks like some kind of monsters with loads of mouths. I like it!
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