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3 Analysis of Anti-counterfeiting Theory
The computer graphics created by fractal theory has extremely irregular and
unsmooth shape and extremely abundant color. Fractal graphics
which can not be
designed by general graphics design software has self-similarity, and graphics created
by general graphics design software are set with classical Euclidean geometry
algorithm, and it can not generate colorful fractal graphics. The dimension of fractal
graphics is fraction, and it belongs to nonlinear technology [5]. If the parameter has
small change, there will be big changes on the fractal graphics. Using these features
of fractal graphics, it is a very effective anti-counterfeiting printing means with fractal
graphics. As long as parameters are not revealed, no one can generate same or similar
fractal graphics. At the same time, fractal graphics have infinite fine details, so they
can not be got by common ways of copying, scanning or photographing by low-end
camera and other means.
3.1 The Anti-counterfeiting Space of Color RGB
The above two fractal graphics are created by Newton iteration. During the process,
the program adopts random function. Every pixel creates random gray-scale values of
R, G, B three color components, and every component value is between 0 and 255.
Then, three components are put together to create a color scheme. In color RGB anti-
counterfeiting space, the size of the space also depends on the size of image. So, the
size of color RGB anti-counterfeiting space is 2
8
×2
8
×2
8
×M×N (M×N is size of fractal
graphics). Therefore, fakers can not create the same picture with original under the
condition of unknown the color scheme.
(a) (b)
Fig. 3.
Fractal graphics drawn by Newton iteration
3.2 The Anti-counterfeiting Analysis of Shape
The dimension of fractal graphics is fraction. Therefore, if the parameters have small
changes, there will be big changes on the fractal graphics.
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