The Application Research on Anti-counterfeiting of Fractal Graphics in Color Printing Based on Newton Iteration and Escape Time Algorithm - Advanced Research on Computer Education, Simulation and Modeling - page 167

z × ( + z

A

)

f ( z ) = = R

Fig. 4. Fractal graphics created by using Newton iteration

A

1 − z

In the formula, parameter A=5, R is a plural, its real part is 5 and imaginary part is
5. Parameters A, real part and imaginary part of R can be set Double type. In Visual
Basic system, the precision of Double type is 15 bit. Therefore, the search precision of
the formula is 10 15 ×10 15 ×10 15 . In color spare, if we do not know the color scheme,
the search precision is 10 15 ×10 15 ×10 15 ×2 8 ×2 8 ×2 8 ×M×N. The parameter A mainly
controls the numbers of petal, and its anti-counterfeiting function is not very well
(Fig.5 shows an example). But, if the anti-counterfeiting function of A is excepted,
the search space is 10 15 ×10 15 ×2 8 ×2 8 ×2 8 ×M×N, it is very big still. The real part and
imaginary part of Parameter R have perfect anti-counterfeiting function, they
change little, very big changes will generate on the fractal graphics (Fig.6 shows an
example). The differences can be detected by eyes and other image processing
technologies.

(a) A=5 (b) A=3

Fig. 5. Different fractal graphics created by different A and the same R