Buddha Slices (Drawing escape time at iteration n instead of iteration 0)

[brainiac94]

I think I've posted on this website once or twice before, and I still hold the opinion that the good old Mandelbrot set is the most fun pattern of them all.
A few months ago while writing yet another program to generate them, I unexpectedly produced something that was reminiscent of the Mandelbrot set, but its "outline" had lots of wild loops and intersected itself in lots of places. I soon discovered that the secret to creating these images is simply following a point's orbit for a number n of iterations before actually drawing the color corresponding to its escape time on the canvas. Varying n leads to different shapes, although at n > 50, they generally lose definition.

My main question is, have any of you seen this before? Does it have a name? Can I claim it?

Here is the product with n = 3:



And n = 8:



I rendered both of these and some more in about 300 megapixels, but due to extremely slow internet, I can only provide that resolution for n = 8, which is my personal favorite: http://87.106.34.86/fractals/Braini8_1Kx_300MP.png (~400MB PNG)
As you guys probably know, this file is huge and will crash your browser, so download it and open it in your program of choice.


Finally, my favorite section of the previous image, in more manageable 14MB PNG: http://87.106.34.86/fractals/hue.png (fixed)


Thanks, hope you enjoy the pictures.

[3dickulus]

it looks very... Buddhabrotty

also reminiscent of some glitchy stuff I ran into while messing around with SuperFractalThing

...but new and different

[brainiac94]

I was actually reproducing this: <a href="https://www.youtube.com/v/y3fwWcV7t0I&rel=1&fs=1&hd=1" target="_blank">https://www.youtube.com/v/y3fwWcV7t0I&rel=1&fs=1&hd=1</a>
The bug was caused by misaligned buffers

Also, if my thinking is correct, the Buddhabrot would be the sum of all these pictures.

[quaz0r]

i guess they are buddhabrot slices?

[brainiac94]

Oh yeah, that's nice and catchy!

[3dickulus]

if they are slices can you stack a few (hundred) together and see?
I think it looks a little different but that might just be because I'm seeing only one slice...
does that (above) slice exist somewhere in the buddhabrot?
maybe you've uncovered a faster way to render this thing, or maybe something all together new, fun to investigate

[brainiac94]

It's definitely not faster. In fact the pictures get lots of artifacts when rendering one point per pixel because the points drift off the grid, so for the big one I calculated 32x32 points for each pixel (!). It took 24 hours to render, on a CPU anyway.

I will stack the pictures when I get some time. I think I have a bunch of them saved in low resolution somewhere

[brainiac94]

Looks about right!

This is adding n=0 to n=8:

[brainiac94]

And n = 0 to n = 42:

[3dickulus]

Ommmmmm yeah Buddha-B

If you have an nVidia card you might want to have a look at cuda-7.5/samples/2_Graphics/Mandelbrot/ in the CUDA SDK for a fast renderer or the perturbation technique used in SuperFractalThing or kallesfractaler

I'm not sure if you have found something new but I am sure that some of the larger math brains here could tell you

[brainiac94]

When I get the time I'll have a crack at writing this in OpenCL. I'm also curious to find out if I can zoom into it efficiently. Hopefully the number of origin points for a specific area can be reasonably narrowed down. Do non-escaping orbits jump between satellites or do they just oscillate between one satellite and the main body?

[tit_toinou]

Can't see the pictures :-( . Could you re upload them ?