  We proposed the deep zoom analysis of the composition of the logistic map and
the tent map, which are well-known discrete unimodal chaotic maps. The deep
zoom technique transforms each point of a given chaotic orbit by removing its
first k-digits after the fractional part. We found that the pseudo-random
qualities of the composition map as a pseudo-random number generator (PRNG)
improves as the k parameter increases. This was proven by the fact that it
successfully passed the randomness tests and even outperformed the k-logistic
map and k-tent map PRNG. These dynamical properties show that using the
deep-zoom on the composition of chaotic maps, at least on these two known maps,
is suitable for better randomization for PRNG purposes as well as for
cryptographic systems.
