I saw a new Ducks fractal variation named Kalisets in this fractalforums post by Kali.

The new variation uses the formula z=abs(z^-1)+c. It turns out this is actually the burning ship formula with power -1 rather than power -2. Like the Ducks fractals the “Mandelbrot” variety (c is set to the value of each pixel prior to iterating) of this formula gives rather boring images, but the “Julia” variety (c is constant across the image) leads to new interesting results.

After trying different variaitons of the formula I came up with these three.

z=log(abs(z^-1)+c)

z=log(sin(abs(z^-1))+c)

z=sin(abs(z^-1))+c

Using the hybrid fractal principal also works fine with these formulas. For the hybrid fractals the formula, variation and power are alternated between iterations.

Higher resolution images are avilable in my flickr Ducks set.

The most interesting thing about these new types of fractals is how the Mandelbrot versions are boring but the Julia versions give rise to these complex patterns and structures. People must have tried these formulas in the past but possibly once they saw the boring Mandelbrot version they gave up and tried other formulas. There are bound to be many more formulas based on these principals found in the future.

The above new variations are now included in the latest version of Visions Of Chaos.

Jason.