Since our original article back in late 2009, the Mandelbulb has taken the world by storm. Programs to render the object have been developed such as Fractal Lab, Mandelbulber, Mandelbulb 3D and many more. It also inspired completely new 3D fractals such as the amazing Mandelbox which exhibits a stunning level of variety.

We've been busy too of course, and this new page presents some of our recent efforts. Many of the pictures shown have a larger version, and can be seeing by clicking the picture. Enjoy!
This is a render of a 'Spine' inside the Mandelbulb.
I've always wondered what a fly-through would look like though, so we went about
rendering some tasty animations. Play the below Youtube videos shown after the picture to see them!

I have a higher quality version of this (800x600 pixels and 60fps) - please contact me to obtain it!

See this one at full size and with the lights off to get the full effect!

Trapped in Mandelbulb Prison

From a distant and unknown part of a certain universe exists an asteroid. Except it's not just any asteroid, but a giant carbon copy of the Mandelbulb set, carved by (even larger) mechanical robots down to an incredibly fine level (apx. 1 trillion voxels cubed).

Unfortunately, upon this asteroid resides a lonely soul, cruelly banished to the place for 800,000 years over some ridiculously minor misendeavour. However, she has made the most of her stay, building some kind of home (a giant tree house would probably be a better description), and has even managed to generate electricity from raw materials found in the crust of the Mandelbulb, along with her knowledge of science.

Around 'Christmas' time, it looks like this from the outside (click pic for full size, then click opened pic again to expand):

At this time of year, you won't find her anywhere near these parts though, as she has much more vital work to attend to and time isn't on her side.

In this world, a dark 'night' like this only appears thrice every 600 'days', and along with it comes a hope of salvation. All other times provide at least moderate daylight by our Earth standards.
Zooming out, we see this below. A thousand potential homes - much alike, but all empty; a sorrowful scene indeed, and not unlike the Earth's place in our own universe. Indeed, our lonely inhabitant occupies around only eighty trillionths of the entire space (volume) of the Mandelbulb asteroid, so it must seem like the universe to her (click picture to enlarge):

Exploration of the Mandelbulb is of interest to our lone wanderer, not least because a certain unknown location holds a secret portal out of this somewhat pitiful existence. It has been said to appear as a faintly glowing pyramid shaped object, perhaps up to two metres in height and two metres across. Why was it even put there?! Is it supposed to be some kind of twisted game by her captors? Or is it maybe to prevent prisoners from losing all hope, and going insane?

Who knows, but one thing is for sure - finding it is daunting, not only due to the sheer size of the Mandelbulb, but also because of the difficulty in navigation by foot. Whether it's getting trapped by falling into a ravine, slipping off a cliff face, avoiding deadly Mandel Nightshade, or overcoming upside-down surfaces, there can't be a more foreboding terrain.

In the daytime, things appear a little more optimistic. Above, every part of the Mandelbulb is coated in a sheet of frost, due to the decrease in temperature compared to night (where the snow melts entirely).

This class of asteroid prison is hollow and in such cases, rumours persist that the much sought after portal is hidden inside the asteroid rather than on the surface. This means finding it becomes much more difficult, especially as the inside is filled with lurking horrors such as this gut-wrenching precipice.

Below is a view from inside too. Due to an incredibly dense type of matter found in the asteroid's crust, gravity on the asteroid's inside is inverted from the outside. This makes it possible to walk 'upside-down' which of course would appear as the right way up for any person inside. Gravity in (or on) the asteroid is generally very strange and can vary dramatically from one moment to the next, especially in deeper, more dense locations. It's also possible to get trapped whilst tunneling from the surface to the inside, so one must be especially careful in this case.
And here below, for the first time, we see the lady herself, homesick and heartbroken, but resolute in her hope to exit this nightmare. If you look carefully, you can see her in the lower-left corner of the screen standing on the green verge. Also apparent in this shot are three lakes (many more outside eyeshot) which do indeed hold vast quantities of drinkable water.

Barely visible in the other shot, here's a closer look at her staring into the vast wilderness.

Maybe this Christmas night, she'll see the glow of the pyramid. Maybe this one. Alternatively, there's only another 799,923 years left to wait.....

Rest of Gallery...

Above: Inside the Mandelbulb is this luminous shot of the spine, with a half-ice, half-snow texture. Click here for the day version, or click the picture for full size.

Zooming out from the purple picture above shows this scene. The spine is less 'developed' due to the lower iteration level.

This render has a jelly/foam/soap like quality (mainly due to the appearance of light scattering underneath the surface).

This spine is the same spine used for the videos seen previously!

Frozen Tornado: Structures such as this are woven into the fabric of the Mandelbulb

More abstract scenes are found in abundance too.

From the mega-large to the microscopic. These tiny 'viruses' measuring only 10e-15m are in the process of replicating.

Here's one of the traps on that aforementioned Mandelbulb asteroid prison that lie ready and waiting for any unsuspecting victim to wander in to.

Many people have remarked on the coral and underwater appearence of the Mandelbulb, and with shots like this, it's not hard to see why.

These two Mandelbulb shells combine like yin and yang.

Just like the Mandelbrot set has a Julia set for every point, the Mandelbulb has a corresponding Julia set for every (3D) point too.

Another Mandelbulb/Julia render. Click pic for full size!

A joint-effort intergalatic attempt to build a giant Mandelbulb resulted in this behometh above. One of the nearby suns (roughly the size of Earth's sun actually) was temporarily moved inside as a way to show off the enormity of their (record-breaking at the time) achievement, and presumably in an effort to encourage more funding for even bigger structures.

A Mandelbulb colossal made entirely out of snow. This was the previous record-holder at 1/4 the size. No dwarf though, as it measures about 3.9e+10 km across. To put that into perspective so that your grandad could understand, that's over 10x larger in diameter than Canis Majoris, the largest known star in this universe. It would take millions of Earth-suns to melt even a tiny pin-prick out of this monster.

This photograph was taken from the aforementioned colossal snow Mandelbulb.

A photograph from the same location 2000 years later shows the 'All-Snow Mandelbulb' was a promotional stunt to woo the public. The truth came out when the snow melted away underneath (with all the water forming a relatively tiny star in the core of the 3.9e+10 km structure). We can now see the strange material they used to originally support all the snow they COATED the structure with.

Skull Valley (above): This popular holiday destination provides tourists a split-path choice. Whether it's the 'icy vortex of eternal despair' that takes your fancy or the 'scorched path of battered rocks' that floats your boat, there's something for everyone in this trip of a lifetime. It's been reported that people love it here so much they never desire to return, or at least never have been seen returning.

Stalagtites: Intricate crystal-like icicles adorn the Mandelbulb's inside.

OpalCalc and this website is copyright Daniel White 2011 onwards. I can be emailed here