Category: Art

A modified Mandelbulb 3d fractal which reminds me of the Idaho panhandle. There is only 1 fractal in this image. The second and third hills are merely copies of the first; the image was reversed for the second hill. Adjusting the color balance toward the blue and the addition of “fog” gives a sense of depth.

green hills of earth

The Green Hills of Earth


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


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.

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.

Puppy Ray is a ray tracing filter included in recent versions of Project Dogwaffle. It can run in the graphics processing unit (GPU) of a computer. I have recently acquired a new machine which allows me to better utilize the GPU. Here are my first two experiments running Puppy Ray in the GPU.

The first is a night scene. I have a particular liking for such images perhaps because I have spent so much time living in northern latitudes where winter nights are so long. I also like the bluish cast common to snowy scenes and the contrast between dark and light. And the lack of illumination can make successfully putting together a pleasing image can be a challenge.

Then one when the sun is up, fjords. Water planes processed in Puppy Ray are semi-transparent, allowing for more realistic rendering; i.e. you can see down into the water. The refraction index of the water as well as wave height and frequency can also be fine-tuned.

Click on the image for a full-sized view.

I have long joked that I am going to form an organization to be called “Chickens Unlimited,” modeled on Ducks Unlimited, dedicated to the preservation of domestic poultry. Chickens Unlimited’s first priority would be the construction of new coops for my flocks of chickens. Yearly memberships would be available; you could even adopt a particular hen, or rooster, and receive a photo of “your” bird and occasional updates about their life.

The Bitcoin and Ethereum digital currencies, aka cryptocurrencies, are probably the best known applications of the blockchain secure, distributed ledger. Issuance of a new digital currency, via an ICO (initial coin offering) is now a common method of raising initial funding for business startups. The value of digital currencies fluctuate greatly. Buy the right coin and you can make a mint.

Cryptocurrencies, as they are digital, usually only exist in cyberspace; however, physical coins do exist. Here is a photo of physical Bitcoins.

phyical bitcoins

Physical Bitcoins

Great news! Chickens Unlimited lives! Here’s your chance to get in on the ground floor. Don’t miss out on the hottest ICO in some time. The KatkaKoin is now available. Build you own digital nest egg.

katkakoin digital currency issued by chickens unlimited

KatkaKoin Cryptocurrency – Chickens Unlimited

Notice that Bitcoin’s circuit board motif has been replaced in KatkaKoin by more appropriate chicken wire (poultry netting). The title KatkaKoin was chosen for Katka Mountain Road in northern Idaho where my homestead is located.

Here’s my latest experiment in combining the best features of Howler and DAZ Bryce. An arctic coastline, perhaps Greenland; with the familiar Flying Moose Aviation de Havilland Otter to indicate scale.

The mountains were rendered in Howler. I really like the degree of control one has in developing the texture, or image map, afforded by the use of an image editor such as Howler. Howler’s 3D Designer has two adjustable light sources which can be of different colors, typically orange and blue shades, resulting in very realistic lighting.

The seaside rocks and water surface were rendered in Bryce. I was not 100 percent successful in integrating the two images; a bit of tinkering will be required the next time to improve the results. This image is a study or sorts; I want to make a similar scene depicting the houses typical of coastal Greenland with a whale breaching in the foreground, and improved floating ice.

Click on the image for a full-size view.

Another new toy! Twisted Brush Tree Studio from Pixarra. More thanks to Philip Staiger at 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

Further exploring Howler’s capabilities I rendered the very same landscape in Puppy Ray GPU as was shown in the last post, having been rendered in 3D Designer. Oh my! Taiga forest, I lived there.

Click on the image for a full-size view.

Rendering Trees in Howler

I use DAZ Bryce quite a bit to render landscapes. A useful feature is the capability to “stack” terrains. Stacked terrains offer a quick way of adding trees or rocks. Here’s a simple mountain terrain rendered in Bryce.

daz bryce 3d mountain terrain

Simple Terrain Rendered in DAZ Bryce

To add trees I duplicate the terrain then modify it in Bryce’s terrain editor. Generally I first add a bit of height and slope noise so the result will be more interesting. The terrain editor can add “spikes” to a terrain bump map. This can be done at several resolutions. In the screenshot of the terrain editor below you can see spikes added to a terrain map. The size and number of spikes generated vary with the resolution chosen. Here the resolution is very low so that you can see the spikes, they are not just dots.  Simple dots would probably render as cylinders, not cones. You can see a rendered view at top right. When rendered in Bryce some of the cones are truncated.

screenshot of daz bryce terrain editor

Adding “Trees” In The Bryce Terrain Editor

When the two terrains are rendered together the spikes of the “tree” terrain protrude through the original terrain. After selecting a texture for the “trees” there are a number of ways to further modify the terrain. By simply raising or lowering the tree terrain relative to the original you can vary the size and number of visible trees. Areas without trees and treelines can be made my editing the  bump map. Such tree layers work best for mid-range or background terrains. With a bit of work you can a quite realistic image.

bryce terrain - spikes, or trees

Same Terrain With Trees

I wondered if I could do something similar in Howler, so I rendered a terrain bump map with spikes, or trees, in 3d Designer; this is the result. The grass color was set as a reddish hue to resemble soil or conifer needle duff. Snow and rock were set as similar shades of green.

example rendering of trees in dogwaffle howler 3d designer

Conifers Rendered in Howler’s 3D Designer

As you can not work simultaneously with multiple bump maps in 3D Designer it would be necessary to edit the bump map to make areas without trees, such as on the peaks and steep, rocky slopes. A better texture map and some method of distorting the trees, so they do not render merely as smooth cones, would improve the results. Post processing might be required to distort them for added realism. I usually have to do the same thing for trees rendered this way in Bryce.

Here’s a de Havilland DHC-3 Otter (which you have seen before), operated by mythical Flying Moose Aviation of Talkeetna, Alaska, flying over a snow-covered mountain range. While Dogwaffle began as a 2D, raster-based paint program, Howler can model landscapes with multiple ray tracing utilities. This image, of stunning, almost photo-realistic quality, was rendered up in the 3D Designer utility. 3D Designer also has the ability to insert localized cloud formations of several types into your image. In this example you can see the leading edge of an approaching snowstorm just beyond the mountains.

outrunning an approaching blizzard

Running Ahead Of The Storm

Dogwaffle has an amazing array features – 2D, 3D, particles. There is also a large and growing number of video tutorials to help you figure out how to use them. Look here for more examples in the future including landscapes rendered with the Puppy Ray ray tracing utility.