Tag Archive: travel


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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An Aeroflot Tupolev (Туполев) Tu-104 passenger jet in flight over a foggy, forested, winter landscape. The Tupolev design bureau logo appears at lower left.

Туполев Ту=104

Tupolev Tu-104 Camel

The Tu-104 (NATO assigned the reporting word CAMEL to this aircraft) was the second jet airliner to enter service, the British de Havilland Comet having been the first. It was the sole jetliner in service from 1956-58, when the Comet was grounded after a number of crashes. The Tu-104 carried over 90 million passengers during its service life with Aeroflot (then the world’s largest airline). The aircraft was retired in 1986.

A number of Tu-104s of various types were used for special applications, including weather research, and as a “vomit comet” reduced-gravity aircraft to parabolic flights allowing cosmonauts to experience short periods of zero gee.

Aeroflot’s need for a modern aircraft with greater capacity and performance than the piston-engine aircraft it then operated by modifying the Tu-16 Badger bomber. The wings, engines, and tail surfaces of the Tu-16 were retained with the airliner, but the new design adopted a wider, pressurized fuselage designed to accommodate 50 passengers. The glazed, bombardier nose of the Tu-16 was also retained, giving the Tu-104 a distinctly military look.

The interiors of Tu-104s built early on were said to resemble Victorian Pullman cars with ornate chandeliers, overstuffed seats, brass serving trays, and chain-flush toilets. But the aircraft, overnight transformed Aeroflot from a lowly-regarded, primarily domestic line, into a major international presence. Those Tu-104s I flew on had a much more utilitarian interior.

Alaska State Ferry

I recently traveled from Haines, AK to Bellingham, WA via the Alaska ferry system. A wonderful, inexpensive way to travel. And you can bring your car.

Met some wonderful folks; especially an interesting couple from Australia. A big “Hi!” to them.

The trip, as well as a drive through the Yukon Territory before catching the ferry, will provide much material for posting on this blog.

The Alaska Marine Highway System M/V Columbia nears Haines, AK

M/V Columbia sails up Lynn Canal

The Alaska Marine Highway System (AMHS), founded in 1948, serves communities in Southeast Alaska that have no road access. Ferries transport people, freight, and vehicles. It has its headquarters in Ketchikan.

The AMHS is part of the National Highway System and receives federal highway funding. It is also a form of transportation of vehicles between the state and the contiguous United States without going through Canada. There are a a total of 32 terminals throughout Alaska, British Columbia, and Washington. The 3,500 miles of routes go as far south as Bellingham, Washington in the contiguous United States and as far west as Unalaska/Dutch Harbor.

The AMHS is a rare example (in the USA) of a shipping line offering regularly scheduled service for the primary purpose of transportation rather than of leisure or entertainment. Voyages can last many days, but, in contrast to the luxury of a typical cruise line, cabins cost extra, and most food is served cafeteria-style.

The AMHS carries around 350,000 passengers and 100,000 vehicles every year. IThe Ferry is very popular with summer tourists (one of the primary reasons Bellingham and Prince Rupert are AMHS destinations). Tent cities commonly sprout up on the aft of mainline vessels, and for budget-travellers, the AMHS is one of the top modes of transportation to the “Last Frontier”. Service drops off significantly in winter. Vessels usually undergo overhauls and renovations during this period due to the decline in passenger and vehicle traffic (attributed to lack of tourists).
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