Page 216 - DCAP303_MULTIMEDIA_SYSTEMS

Multimedia Systems

notes he observed occurring in many different structures. These patterns appeared nearly identical
in form at any size and occurred naturally in all things. Mandelbrot also discovered that these
fractals could be described in mathematical terms and could be created using very small and
finite algorithms and data.
Let’s look at a real-world example. If you look at the surface of an object such as the floor currently
beneath your feet, you will notice that there are many repeating patterns in its texture. The floor’s
surface may be wood, concrete, tile, carpet, or even dirt, but it still contains repeating patterns
ranging in size from very small to very large.
If we make a copy of a small part of the floor’s surface and compare it to every other part of
the floor, we would find several areas that are nearly identical in appearance to our copy. If we
change the copy slightly by scaling, rotating, or mirroring it, we can make it match even more
parts of the floor. Once a match is found, we can then create a mathematical description of our
copy, including any alterations we have made, and can store it, and the location of all of the parts
of the floor it matches, as data.
If we repeat this process for the entire floor, we will end up with a set of mathematical equations
called fractal codes that describe the entire surface of the floor in terms of its fractal properties.
These mathematical equations can then be used to recreate an image of the entire floor.

The process illustrated in this example is very similar in concept to vector (2D) and 3D graphics,
where mathematical descriptions of objects, rather than actual pictures of the objects themselves,
are stored. The important difference between vector and fractal graphics is that fractal descriptions
are derived from actual ecofactual patterns found in real-world objects, while vector and 3D objects
are purely artificially generated structures that do not naturally contain fractal patterns.
Fractal encoding is largely used to convert bitmap images to fractal codes. Fractal decoding is
just the reverse, in which a set of fractal codes are converted to a bitmap.
The encoding process is extremely computationally intensive. Millions or billions of iterations are
required to find the fractal patterns in an image. Depending upon the resolution and contents of
the input bitmap data, and output quality, compression time, and file size parameters selected,
compressing a single image could take anywhere from a few seconds to a few hours (or more)
on even a very fast computer.

Decoding a fractal image is a much simpler process. The hard work was performed finding all
the fractals during the encoding process. All the decoding process needs to do is to interpret the
fractal codes and translate them into a bitmap image.
Two tremendous benefits are immediately realized by converting conventional bitmap images
to fractal data. The first is the ability to scale any fractal image up or down in size without the
introduction of image artifacts or a loss in detail that occurs in bitmap images. This process of
“fractal zooms” is independent of the resolution of the original bitmap image, and the zooming
is limited only by the amount of available memory in the computer.

The second benefit is the fact that the size of the physical data used to store fractal codes is much
smaller than the size of the original bitmap data. If fact, it is not uncommon for fractal images to
be more than 100 times smaller than their bitmap sources. It is this aspect of fractal technology,
called fractal compression that has promoted the greatest interest within the computer imaging
industry.
Fractal compression is loss. The process of matching fractals does not involve looking for exact
matches, but instead looking for “best fit” matches based on the compression parameters (encoding
time, image quality, and size of output). But the encoding process can be controlled to the point
where the image is “visually lossless.” That is, you should not be able to notice where the data
was lost.

210 LoveLy professionaL University