New Scientist Features the Mandelbulb

I discovered an article in the latest New Scientist magazine about Daniel White's Mandelbulb. Found it really cool as I've been working on this stuff quite a lot recently! Read the whole article here at New Scientist!

Ray Tracer in AS3: Rendering the Mandelbulb in Flash

So I went off for a few hours and thought how I could improve the voxel engine. Both from an efficiency perspective as well as that of realism.

I realised that the only route was ray tracing and after reading this fantastic article by SuperJer about his pixel machine experiment I was motivated and inspired to try something along these lines for my renderer.

The article takes the creation of a ray tracer from its very early stages to a really polished program. All this happens in one weekend by the way, I really suggest you read it.

Anyway the idea behind raytracing is that a ray of light is passed from your camera through a pixel on the screen. The ray formed between the two points continues to pass through your scene until it hits something. When it hits something the pixel through which the ray passed is updated with the colour value of the object it hit, or failing that the colour of the sky behind, and a ray is "fired" through the next pixel until your image is formed.

So in my case I'm trying to render the Mandulbulb set. Something I've now done many times before, but lets be honest, in the past I've needed huge numbers of voxels and the results weren't great. So what happens in the ray tracer?

1. I fire a ray through the current pixel - starting at 0,0 working all the way to the image width/height.

2. I check along the length of the ray to see if that location is a part of the Mandelbulb Set.

3. If it is - check if that point is in light or shade.

4. Fire another ray from this point to my light source.

5. Check a bit away from this point in the direction of the light source, if that point is also a member then any light from the light source would have been stopped. So shadow the pixel.

6. Otherwise colour the pixel normally.

The resulting images that are built up show a lot more detail. Not only that they have pixel perfect shadowing, perspective, rotation and you can't see any stupid voxels.

Lets take a look below at some ray tracing in flash. Below you can see increasing resolutions from
137 x 100 to 1100 x 800 pixels.

And below is one I left to render for about an hour (2200 x 1600 pixels). Just click to enlarge it!

Inverse Mandelbulb Pixel Mapping in Flash

When we map the 2d Mandelbrot Set we normally colour a pixel depending on the rate at which that point tends to infinity on some colour scale. In 3D normally this wouldn't work - where you have solid objects you'd be changing their colour internally. But since we are looking at cross sections using the voxel renderer it is actually very doable. Here are a few examples:

Remember that the inverse is being mapped. I really like the effect, and its definitely nice to add some colour to the dull grey images of the previous post.

Its like looking into a three dimensional cave of fractal goodness. Another possibility would be to use transparent pixels and change transparency levels. I will give this a go next as it would allow the whole shape to be seen externally, with colour (possibly? we'll see!)  Anyway click here to see all this fractal goodness happening in real time in flash using AS3! Enjoy

Working - 3D Mandelbrot in Flash

Possibly a world first, I don't know, but I can confirm that I have rendered Daniel White's Mandelbulb set using AS3.

The first render is 216 Million voxels (600*600*600) and took about 10 minutes to do.

This is the 8th order of the Mandelbulb (where things start to get interesting from a fractal detail point of view).

First screenshot is half way through the rendering process:

And here is the finished product:

Hopefully soon I'll have a 3D Mandelbrot Explorer ready and working much like the 2d version previously. I'm currently rendering an image 1000x1000x1000 voxels in size (1 Gigavoxel), and I'll add it to this post when it comes out!

edit: here is the gigavoxel render (zoomed in a bit too much though which I'm annoyed about so it cut off the "colosseum" structure at the top!

here is a quick preview of the voxel engine rendering a lower resolution (400x400x400) version.

To zoom in at the moment you'll just have to right click and press "zoom in" but this won't actually zoom in, just give you can enlarged version. Worth doing if you want to see individual voxels though :)

Enjoy!

edit: Just started playing with zooming and rotating:

Here is a view of the colosseum structure (normally at the top) from the side:

First Demo of the Mandelbulb in flash.

So I've put together a demo of the Voxel Renderer doing something - not entirely sure if it is the true Mandelbrot in 3d - but  click the image below to see the approach I'm taking -

Zoom in and you'll see how it's constructed from isometric cubes.

Mandelbulb - First Thoughts

In light of Harry's comment I thought I'd take a look at trying to code a Mandelbulb set.

The first obstacle was how to render:

The examples I've seen mainly use ray tracing - there is no way as3 is capable of raytracing this kind of complexity within my lifetime. I decided to write a simple voxel (3D pixel) engine to display the set. The theory behind this is fairly simple. Work in isometry (no perspective), render from left to right, bottom to top and front to back and all should work out.

Just so I knew the kinds of things I was looking for here are a few of Daniel Whites original renders of the Mandelbulb.

So quite something to aim for with flash!

Anyway, I thought I'd start BIG, and by BIG I probably mean I regret doing it now because of the insane render time. Poor flash player.

As I write this the whole render (1000x1000x1000 - 1 million voxels - 1 mega voxel!) is about 2 percent complete. I don't know whether what I am rendering is the right thing or not but hopefully as more shapes begin to unveil themselves it will become clear and I'll know whether to start again or not!

Here are a few renders using the Voxel Engine:

The first few cross-sections - some potential? We'll see..

About 10 cross-sections down - only 990 to go! There are some interesting shapes going on though - note this is a zoom. You can see the individual voxels and how I build them up quite nicely. There does seem to be an awfully regular plane forming which shouldn't be there.

Yet more complete - starting to get some nice inwards curving - hopefully it will make a shape thats kind of spherical...

Just a bit more - about an hour down and the stage I go to bed at! I'll take another look in the morning - until then good night!

Below is what I found the next morning: Not exactly what I was looking for - fractal? possibly - but not nearly as complex as the Mandelbrot I should have been getting.

Unfortunately this means I'll have to change the settings and start over: at least I know the Voxel Engine works, and that I shouldn't do quite as ambitious renders! I'll keep you updated on the results!