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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 . 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).

oh yeah, this is what i call a nice object !  O0

Nice one Ron !
I have an idea for doing a pseudo-Newton ;)

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.

Ohhh pretty...  hmmm... have to slice these things open and see what makes 'em tick!

@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 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

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.

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.

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).

also a great variant :D
I really like them a lot!

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