Tag Archive: Space


An icy moon orbits a frozen world. You can decide which is which.

mandelbulb 3d fractal landscape example

An Icy Moon in Orbit Around a Frozen Planet

The mountains in the image above are merely a rendered 3D fractal. If you are not familiar with fractals they are never-ending patterns, infinitely complex patterns that are self-similar across different scales. In other words, as you enlarge a fractal you will see the same, or very similar pattern emerge repeatedly ad infinitum as you enlarge the original fractal. This is called expanding symmetry or evolving symmetry. You are already familiar with fractal patterns, the natural world is full of them. Take a tree, as a simple example. The pattern of the trunk and branches and secondary branches is repeated as you move to the scale of branches, secondary branches and twigs. Another example would be the tiny rivulets of rain or melting snow water running onto successively larger flows until they are a large river emptying into a sea. Physical laws dictate that flowing water moves in similar ways at all scales. The same thing is true for coastlines at any scale; similar patterns reappear over and over and over as you look at ever smaller scales. As a result it is practically impossible to actually measure the exact length of a coastline.

The math behind fractals is very complicated, and I don’t understand it anywhere well enough to explain it. Even the experts are not in complete agreement as to how they should be defines. Even Benoit Mandelbrot, who is generally credited with developing the modern idea of self-similarity, fractals, in nature, once characterized them as, “beautiful, damn hard, increasingly useful. That’s fractals.” If you want to impress people at a party with how smart you are repeat Mandelbrot’s 1982 definition: “A fractal is by definition a set for which the Hausdorff-Bescovitch dimension strictly exceeds the topological dimension.”

So, enough with the heavy-duty science. You can find much more about the science of fractals on the Internet. I generally think of fractals as coming in 2D and 3D varieties. I do some work with both types, examples of which have appeared on this blog. 2D fractals are generally backgrounds or some other element; with the 3D fractals often being the mountainous terrain generated by various software packages.

Abstract, 2D fractals can be generated by a computer calculating a simple equation over and over. Here are a few examples, all made with the Apophysis fractal generator:

multicolor apophysis fractal

Brainstorm

swirling, multi-colored apophysis fractal

Gravitational Blueshift

orange and green apophysis fractal with a starry background

Quantum Entanglement

multi-colored apophysis fractal

Structural Iridescence

Then there are 3D fractals. I used a free software package called Mandelbulb to create the examples in this post.

This is a very simple one in which the 3D nature is evident:

simple mandelbulb 3d cube fractal

Simple 3D Cube-Style Fractal

Of course, 3D fractals can be much more involved:

blue mandelbulb 3d fractal

A Blue Hatch, A Red Atmosphere

red-toned mandelbulb 3d fractal

Alien War Helmet

And one I like very much – a habitat on a rocky moon or asteroid. The fractal reminded me of the cartoon-like atmosphere of some of the stories by the great Polish science fiction writer Stanislaw Lem, author of Solaris, The Cyberiad, Tales of Pirx the Pilot, and many others. I added a few elements to complete the scene including a spaceship Pirx would have been proud to fly.

modified mandelbulb 3d fractal in memory of stanislaw lem

Stanislaw Lem Station

Science and art! Cool, eh? You can do this too.

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Another new toy! Twisted Brush Tree Studio from Pixarra. More thanks to Philip Staiger at thebest3d.com for telling me about it. With Tree Studio you can quickly create 2D trees of several deciduous and conifer species.

A few trees made in Tree Studio added to the recently-posted image of a de Havilland Otter flying over snow-covered mountains gives it an entirely different look and feel. With a bit of work you would have a very nice forest at feet of the mountains. Tree Studio allows you to adjust the colors of the leaves as I have done here so that the birch trees can be in their autumn colors.

Click on the image for a full-size view.

For added realism a few of the png tree images generated by Tree Studio have been warped with another application.

Here is a screen shot of Tree Studio. The leaf color had been changed from the standard green to yellow. Tree Studios works with layers. A layer for the background, a layer for ground cover if, a layer for the trunk, a layer for the leaves. So that trees in the foreground will appear more realistic I suggest deleting the ground cover layer and adding another leaf layer behind the trunk as in this screen shot.

screenshot of Pixarra twisted brush tree studio

Twisted Brush Tree Studio

Orbital Tuber

I have met people who do not believe Idaho is a real place. Others know it it is somewhere in flyover territory, but can not place it any better – “Isn’t that somewhere near Nebraska?” Mostly, people just think it is a backward place. Not true! Idaho has a space program and placed a satellite in orbit.

Spudnik - 1 Orbital Tuber

Spudnik – 1

The scientists and engineers at the Idaho Space Authority dubbed it the Idaho Geosynchronous Agriculture and Forest Fire Observation Tuber, or IGAFFOT for short. IGAFFOT does not exactly roll off the tongue so the governor sponsored a satellite naming contest among the state’s elementary school students. There were a number of suggestion including Tater Tot, but almost 99 percent of the students suggested Spudnik; and so it was.

During a television interview the director of the Idaho Space Authority explained that potatoes make wonderful observation platforms as they can be mass-produced locally and generally have several eyes. In addition, when the orbit decays the tuber is re-entry baked by friction with the atmosphere. All you need if you find one of these satellites after it comes down is butter, salt and pepper; with maybe a bit of sour cream.

I was able to obtain an example of the cloth mission patch:

Spudnik -1 Cloth Mission Patch

Spudnik -1 Cloth Mission Patch

And now for something completely different.

I don’t know if you’ve seen them; those pictures taken by NASA’s Cassini probe of the geysers on Saturn’s sixth largest moon Eneceladus. If not, look them up on the Internet.

Enceladus is one of several moons of the outer planets which have water oceans under their surface ice. The scientific community believes life may exist in Enceladus’ ocean; it contains salts and organic compounds.

Anyway, I’ve got some friends who have been there (They are not exactly from around here); they brought me some photos – here’s one:

Artist's conception of life on Saturn's moon Enceladus

Under the Ice of Enceladus

Click on image for full-size view.

Lot’s of living things there though my friends tell me the terms “plant” and “animal” don’t exactly work to describe them.

Though it is heated by gravitational stressing and radioactive decay the water is rather frigid – that’s my excuse for including it on this blog.

Sometimes the simplest fractals work really well.