Why are fractals important? Because Leonardo Da Vinci realized that the components of trees are fractions of the whole. Each part of a tree is a smaller copy of what came before it. For example, as a tree grows, the new new growth is a fraction of what it grew from such as branches from a main trunk. If there are two they will each be half the size of the trunk, if there are three, each will be one-third the size. Apply this same concept to other vegetation and you begin to see how it can be applied for military use.

Because fractals are so common in nature, they have become the next big thing for camouflage. How it works is that a natural shape is combined with itself over and over to make bigger versions of the same shape. By extension, since it is a natural shape, it should fool perception. In many cases the colors will change, but not the basic geometry. You *could* (and people desperately have) make an argument that the recent pixelated camouflage rage is fractal based but the square isn’t exactly something you regularly run across in nature. Since the Army should be announcing the down selects for their Camouflage Improvement Effort soon, we can’t wait to see if any of the patterns are truly fractal in nature (and if the military’s fascination with patterns of squares has finally run its course).

Correct me if i’m wrong, but isn’t the Italian Army current issue camouflage based on a digitally-generated fractal pattern?

There are a lot of patterns out there that use fractals, both foreign and domestic.

My issue with the term is that companies are referring to pixelated patterns as fractal patterns because they are using the same shapes over and over and combining small squares to make big squares. This isn’t exactly the concept. The point is to use a fractal derived from nature in the hopes that it will trick the brain into assuming it is in fact, natural.

I’d say that at this point, every pattern is going to technically be “digital” simply because it was created on a computer. The term digital becomes redundant.

Thanks for the follow up.

Fractals were the next big thing almost a decade ago, with Guy Cramer complaining about the CADPAT pattern that was cutting edge at the time. He suggested using fractals to define the element distribution of a pattern, as opposed to CADPAT’s basic texture matching.

Fractals aren’t a camo panacea. You can’t put a Sierpinski triangle on a uniform and expect better results, though it is a fractal. It’s the proper application of mathematical, visual, and psychological principles to match the specified environment that really counts, fractal concepts are merely involved in the process. That’s just for concealment; then you have to worry about disruption. (IMHO, neither raw fractals nor texture matching can achieve satisfactory results alone, but that’s just, like, my opinion, man)

With the issue about squares and fractals, you are correct in that one can not view an entire fractal by using squares of a set size. One can only view an image of a portion of a fractal, represented on a limited media, whether it be the pixels on a computer screen, or the pixels on a uniform. Both displays are meant for a certain viewing distance, and if you can see the pixels, you are too close! For patterns on most combat uniforms one shouldn’t rely on the pattern to conceal one’s self any closer than 5-10m as a result, so the wearer shouldn’t go for any frontal H2H ambushes in open areas under normal circumstances.

This is how camo like Hyperstealth makes has a fractal-based pattern that retains the CADPAT-style pixel aesthetic: the uniform displays what it’s able on the area that it’s able for a viewing distance of normal combat ranges. Viewing distance is an important consideration here, and it doesn’t much matter what shape the “pixels” are at such ranges (because at they’re so fuzzy at that range that it doesn’t matter), merely their size, color, and placement.

Like I’ve said before, thanks for the camo coverage (it’s a favorite subject of mine), and I’m anxious to see the Army program’s results!

I am a college student working on the same concept. Fractals and mathematics in nature have always interested me. I am trying to figure out ways to incorporate some of those principles into making more effective camouflage. Using a program that samples colors from a user’s image or aerial photography, I generate the exact paint codes needed to Cerakote equipment.

By using aerial photography to generate colors for the area of operations, you get a “multicam” color combination of the region that works incredibly well. This applies to urban and suburban settings too. You tweak the program to ignore rooftops, clouds, and streets that would contribute to colors not seen on the ground. It shouldn’t matter how far you zoom in or out- because of fractals in nature, the ratio of colors will stay the same!

Here is a sample image generated, with no changes to the computer selected colors. The shapes are generic blobs in this version. The aerial image is a portion of Afghanistan.

http://i19.photobucket.com/albums/b157/paintcomp/afghanistan.png

The next image is from a portion of the Southwestern United States. This time the shapes have been pixelated, a basic type of fractal. Results are good, even though the ratio between colors has not yet been implemented. You may also notice the available colors of Cerakote start to fail in this geographic location. This can easily be solved by mixing colors to match the true values.

http://i19.photobucket.com/albums/b157/paintcomp/southwestusa.png

The next step will be to generate the fractal pattern itself, using shapes and geometry found in nature. I’m using techniques straight from Chaos Theory, manipulating organic shapes and layers to form a 3D pattern that works far better across different distances. The fractal shapes change depending on location, with a rocky area and a forested area having very distinct iterations. You can think of it as a multi-color, multi-distance solution. It’s similar to blurring found in modern camouflage patterns like multicam, A-TACS, Kryptek LEAF, PenCott, and Ghostex. But by using organic fractals and specific colors tailored to the area of operation, it greatly increases effectiveness over these techniques.

Of course this would result in more needing more fabrics for specific areas, but the camouflage cannot be beat (short of a ghillie suit with natural vegetation mixed in). Until a color changing material can be created cheaply, this is the best solution.

Shoot me an email at mlloyd1@gmu.edu if you would like more details.

Wonder if the’re looking at the new Kryptek Camo? Their “Highlander” camo has Army written all over it.

I have some things about fractals to say.

First, term “fractal” could refer to many things: stochastic patterns (fuzzy spots), branching patterns, and, absolutely not all of them could be a good camo.

Second, self-similarity and scale invariance of some fractals could be a really great property of camo pattern, because the object, covered with such camouflage, could be observed from almost any distance, and pattern will work anyway regardless of angular size of an object. Currently, only the Pencott, new Finnish camo or variants of Flecktarn has something like this. Most other “fractal” patterns has very small details and blends to single color when observed by unaided vision from relatively small distance, and there is only thing to rely – a chance, that resulting solid color will not be very different from the surrounding.

Third, lets do a simple experiment: look at some single tree in winter. If you are not 100% city guy, you will immediately be able to say, if it is ash, poplar, linden or aspen. Even if you can’t describe the difference, you could see all that small details of branching form. The same situation is with camo patterns – people are sensitive to some natural fractal patterns and are able to understand, that something is different than surrounding objects. It’s better to be careful, using branching textures (like some hunting camo patterns).

Fractals are to camouflage as a bicycle is to a fish – of no use.

A tree is not a larger version of a leaf.

The Fractal Dimension (fD) is a different matter all together.

The fD describes the textural roughness at each scale.

Ideally start off by measuring the fD of the environment.

Then generate “noise” to match the fD.

Bear in mind that only the edges of the noisy blotches are of interest. The colour the edges are filled with is not really important as long as they meet the environmental statistics.

The texture matching and shape disruption patterns can be integrated easily, if you know how – this is the hard part.

Using squares for the pattern elements just comes down to simplifying the calculations.

Theoretically it is possible to make a pattern which is both texture matching and shape disruptive using “naturally shaped” objects, but in practice this is near impossible.

I use fractal math daily in making computer graphics imagery for the movies and it is by far the most valuable and simple method or mimicking the randomness of nature. From the random densities and shapes in fire, smoke, clouds to the distribution of pebbles and rocks on a hillside, it’s very much the language of nature (that and L-Systems). It doesn’t surprise me that fractals would play a part in camouflage design.