Burning Ship Mandelbulber 1.21 OpenCL Custom Formulas

[mclarekin]

Here is a basic Burning Ship Mandelbulber 1.21 OpenCL Custom Formulas

[mclarekin]

Here is the image

[mclarekin]

Forgot to mention,  picture was a power 2 mandelbulb burning ship.

Here is a zoom on the x-axis

[TheRedshiftRider]

Wow, it looks amazing. I normaly dont really care about 3d fractals but this is amazing!

[matsoljare]

The middle right looks especially interesting there! The lower right too!

[mclarekin]

Well it might look amazing and interesting but  a closer inspection of the detail is not the best in some areas. I remember now that when I first did the burning ship mandelbulber I added Mandelbox rotation to the iteration loop that sort of fine tuned it a bit as well as using low DE step factors of 0.1 or less. Which equals long render time, so impatient me went back to IFS types. I suppose I know more now and should experiment again, but will wait until I have a faster computer


The rotation can make interesting renders, attached shows the burning ship masts have now almost disappeared, so a flatter less messy surface without the fattening that would of happened if I had just reduced the Detail Level instead

[mclarekin]

This is what I meant by fattening. Same original image with Detail Level (quality) set down to 0.1 and DE step factor 0.1. And still there are bad area (over stepping?)

At 800 x 600 the render took a horrible 7 minutes . (would be approximately 20 times longer at 3200 x 2400 )

[mclarekin]

Attached is the burningship mandelbulb from pwr2 to pwr9

[youhn]

Nice to see how the higher powers start to look more alike their twins in the normal mandelbulber. The lower powers like 2 and 3 seem to have a more unique identity. This observation is based on the overall shapes (zoomed out). While fractals promise similarity (you keep getting more of the same stuff when zooming in), this is NOT what we see in certain fractals. They display a very wide range of shapes. The basic method (?) of shapes could be categorized. For example the Mandelbrot family have curves (spirals, circles, bulbs, equipotential lines) as one of the basic shapes, while all the burning ship variant (with the absolute operation in their formula) show sharp corners. We might have to rethink the definition of fractals based on our observations.

[mclarekin]

@youhn. Yes, now that you point it out, maybe fractals with self similarity should be called "self similar" or "pure" fractals or something more mathematical.

I've always thought of the burning ship as a "modified" Mandelbrot with the data being continuously thrown back towards one quadrant.
Which is different to the other "modified" fractals that retain a high degree of self similarity like Mengers with folding, rotations and scalings added.

But then the burning ship becomes more self similar as the effect of increasing the power reduces the effect of the Absolute function.

The definition of  "some degree" of self similarity"?

All to tricky for me.

[mclarekin]

Here are vertical views pwr3, pwr4, pwr5 & pwr9 standard  Mandelbulb and the burning ship type Mandelbulb,  showing the absolute function's influence decreasing.

[cKleinhuis]

hey mclarekin, the self similarity is described with the self similarity dimension, by mandelbrot

the burning ship is very self similar in a way that the burning ship reappers endless times, the border of the mandelbrot has dimension 2 which means it is a very complex line, the burning ship induces some straight lines through the abs() method, mandelbrot is king in terms of complexity, burning ship is equally interesting anyways because of different shapes

my five cents

[youhn]

You mean the Hausdorff dimension? It's not the degree of similarity, but more a degree of roughness. Mister B Mandelbrot prefered this word over self-similar.

I've always thought of the burning ship as a "modified" Mandelbrot with the data being continuously thrown back towards one quadrant.

Exactly right. This is why it would be correct to say that Mandelbrot set and Burning Ship set are close family, based on the process. But this small change in the process leads to some very different results. Just as our DNA is about 98% equal to that of chimpanzees or bonobos. But I like to think we are different, not only different family but another species.