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Guys, raymarching renders with negative powers (-2 and below) in the trigonometric Mandelbulb formula also gives interesting results.

My CUDA/Optix implementation essentially permits realtime sweeps though various parameter sets. First I tried smoothly sweeping exponents +1 to +10, then I let it backwards sweep exponents to -10 and the resulting shapes were also quite interesting. In fact, almost as interesting as the positive powers.

Christian

You need to choose a smaller raymarching step factor (e.g 0.1) in front of the DE term and not the usual 0.5. Set your iteration count somewhere in between 5 and 9 for a start.  I personally like the 5 cutoff best.

For odd iteration cutoffs, the resulting shape will be hollow (you can see through holes in the exterior). For even iteration cutoffs, the bulb appears solid from the outside. So for odd iteration count, this appears to be a disconnected set. I would love to fly right through it with my camera to explore it from the inside, but my current raymarching approach is not suitable for this.

Because the hollow shapes would pass as chandeliers, I would hereby like to coin the phrase "mandeliers" for these things. Let's see if it sticks ;)

(http://img340.imageshack.us/img340/2120/mandelier.jpg)

These are just some first observations.

Power -1 results in some concentric toruses. (two sided shape)  With one iteration, you get a donut. With two iterations you get a donut and a ball. Three iterations gives two toruses. Four iterations gives two toruses and a ball. So an even iteration counts always generates some object in the center.

Powers -2 and onwards are more bizarre. Power -2 is three sided, and the torus rings now appear on each side.

Power -3 is four sided, and so on. The torus rings get more and more distorted the lower you make the power.

For large negative powers, this thing ressembles a ball more and more. The mandeliers remain hollow for odd iteration cutoffs.

Hey, I've discovered something new! To boldly render what no man has rendered before....

Christian

That leads me to think; Does it converge to a solid or a hollow object? Is infinity odd or even?

Is god a man or woman?

I guess we'll only have God's thumbprint (aka the Mandelbrot set) to investigate.

umm, please don't think you're the first person to think of putting a negative (and non-integer) value for the exponent, some of us have been doing this for years ;)

more generally, i don't think everyone is posting every observation they make about this thing; personally i'm losing track of all the millions of little sub-threads that have since been posted :S