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cool julia worms ! and i also can spot minibrots !

great work! 

As usual, great images from our Supernova specialist
This one is my new desktop background, I would have named it "Attack of the Elephants' parasites"

Another Supernova image, inspired by Pauldelbrot's findings:

Amazing image, bib, I think it's even better than Pauldelbrot's image (sorry Paul , but still nice work)

Quote from: me, months ago

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One day I thought it would be nifty if the lake shapes in Antimatter fractals were more varied. In particular, if they could have petals. So I decided to make zero stop being always a superattracting fixed      point.                                                                                                                                                                                                                                                                                               
                                                                                                                                                                                                                                                                                                       
Antimatter is the family of mappings z². Supernova just adds an innocent little "+ b" to that, not unlike how Nova was derived from the Newton's Method Julia fractal whose attractors were the roots of z³ - 1.                                                                                                                                                                                                                                                                                             
                                                                                                                                                                                                                                                                                                       
That innocent little "+ b" unleashes a veritable flood of exotic new forms. Of course the system remains capable of producing the full gamut of interesting dynamics, including Herman rings. The addition of a constant does not change the partial derivative with respect to z, so the critical points remain the same. However, only infinity is a permanent attractor now; zero superattracts only for b = 0 and for other    b-values is an "interesting" critical point. The fixed point moves away from zero, though it still attracts for small b and small enough c.                                                                                                       
                                                                                                                                                                                                                                                                                                       
In fact, the c-plane develops a Mandelbrot set looking like the original, but scaled and rotated depending on b, as viewed using the critical point zero as the lens. The most interesting images, however, come from studying one of the "usual" critical points for Antimatter, within the region near the border of the (now-"ghostly") Zero Mandelbrot. In these regions, the characteristic "lakes" in the centers of seahorses and similar structures implode as the attractor bifurcates and eventually disintegrates.                                                                                                                                                                             


(Apologies for the slightly wacky-looking quoting; the quote tag seems to screw up LaTeX display for some reason, necessitating a workaround.)

Ultrafractal is really easy to do that it took me 5 minutes to implement. My next animations will be based on this formula.
 I am visually (not mathematically) studying the dynamics of both C-plane and B-plane fractals in order to choose some interesting dynamic features to show. Stay tuned!

Supernova-Cplane {


init:
  z = @start
loop:
  z = @b+@a*z^@power * (z-#pixel) / (1 - #pixel*z)
bailout:
  |z| <= @bailout
default:
  title = "Supernova C-plane"
  center = (-0.5, 0)
 
  param start
    caption = "Starting point"
    default = (0,0)
  
  endparam
  param power
    caption = "Power"
    default = (2,0)
  
  endparam
  param a
        caption ="a*"
        default = (1,0)
  endparam
  param b
        caption ="+b"
        default = (1,0)
  endparam

  float param bailout
    caption = "Bailout value"
    default = 4.0
    min = 1.0

  endparam

}

Supernova-Bplane {

init:
  z = @start
loop:
  z = #pixel+@a*z^@power * (z-@c) / (1 - @c*z)
bailout:
  |z| <= @bailout
default:
  title = "Supernova B-plane"
  center = (-0.5, 0)

  param start
    caption = "Starting point"
    default = (0,0)

  endparam
  param power
    caption = "Power"
    default = (2,0)
  
  endparam
  param a
        caption ="a*"
        default = (1,0)
  endparam
  param c
        caption ="c"
        default = (1,0)
  endparam
  float param bailout
    caption = "Bailout value"
    default = 4.0
    min = 1.0

  endparam
}