The other day, I went to look something up in Wikipedia, and noticed that their featured image was a thing called a Mandelbulb.

Ages ago, back at the tail end of the ’80s, an actuary I worked with, who was into “recreational math” (whatever *that* is), introduced me to the Mandelbrot set fractal. He was good at explaining things to the mathematically-challenged, and I have it by the tail, but not well enough to explain it to anybody else. What, for me, was more interesting than the math, was the ability to generate these gorgeous, colorful pictures.

The Mandelbrot Set

There is infinite detail around the edges of the black area, and you can zoom in on an area and create some amazing images.

Mandelbrot Image

The above images were generated by Fractal Explorer 2.02

So this Mandelbulb thing caught my attention. It’s a 3D fractal.

The Mandelbulb 3D Fractal

I did a search and found a package called Mandelbulber which can be used to zoom in on areas of the bulb and generate some interesting, sometimes organic-looking images.

Mandelbulb Image

Mandelbulb Image

The above images were generated by Mandelbulber (Windows) 1.18.

Mandelbulber runs on several operating systems and I tried out both the Linux and Windows versions. The Windows version seems faster and produced better images, but that may be because my graphics card manufacturer has never bothered to write a driver for Linux.

Image rendering really warmed up my CPUs. I have an old PC with only two cores and they were both running at 100%. Oddly, there was hardly a blip on the GPU, so the process must be mathematically intense.

I’ve only been messing with this for half a day and not at all with the color possibilities. There are some fabulous images (and an article) by Daniel White, one of the guys that came up with the formula, at http://www.skytopia.com/project/fractal/mandelbulb.html. Arthur C. Clarke explains the Mandelbrot Set quite well (and in plain English) in his *The Ghost from the Grand Banks* and there’s a book by James Gleick, *Chaos: Making a New Science*, that also discusses the Mandelbrot Set. Unless you’re into “recreational math,” don’t bother with the Wikipedia articles. They are composed entirely of mind-numbing formulae.

This is so fun!

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good lord! WHAT ARE you talking about? but you ‘took’ those pixures, right? many (seriously, a couple dozen) years ago a couple of my I T – intensive work mates got swept up in whatever this is. and, dumb kwestyun #3: is there (ahem!) an actual “use” for this? (i’m afraid that there is). still, i’ll have to re-read but i think i’ll fall into the kwyk-sannd if i pursue your link!

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Fractals can come pretty close to mimicking nature. If you compare all the leaves on a tree, they are similar but not identical. The swirls in my Mandelbrot image have that same kind of self-similarity. One “practical” use is generating world objects (trees, rocks, shorelines, mountain ranges) in 3D video games – faster and easier than “drawing” each leaf.

You’d stand a better chance than me at understanding the math – I can barely balance my checking account, but don’t engineering and physics require a good head for math?

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(allegedly !) let’s just say i’m often “aware” of math, not necessarily having the cranial gears ‘n wheels whirring away, per se.

but, you TOOK those pixures, somehow?

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Well, I think

foundwould be better thantook. The software (Fractal Explorer for the 2D Mandelbrot and Mandelbulber for the 3D Mandelbulb) allows the user to frame and zoom over and over until you are looking at something that’s one gazillionth the size of the original. Then you mess with the colors and save a .jpg. Because the images are generated by static mathematical formulae, they alreadyexist, but theoretically, you could zoom infinitely and still find new detail, sofindinga particular image would require that you know the specific coordinates and scale. A computer can’t handle infinity, and even the most powerful massively parallel supercomputer has limits on decimal places, so at some point, your image becomes pixelated. But you can still zoom to a scale where the original would be measured in square miles.You should give it a try – both packages are free. FE runs only on Windoze, but Mandelbulber is available for Linux too.

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