Different asymptotic behavior versus same dynamical complexity: Recurrence & (ir)regularity

The asymptotic behavior of N-adic complexity

We study the asymptotic behavior of stream cipher security measures associated with classes of sequence generators such as linear feedback shift registers and feedback with carry shift registers. For nonperiodic sequences we consider normalized measures and study the set of accumulation points for a fixed sequence. We see that the the set of accumulation points is always a closed subinterval of...

Dynamical behavior and complexity of Langton's ant

O ne of the first models of artificial life, proposed back in the 1980s by Christopher Langton, founder of the field, was the virtual ant [1,2]. This simple cellular automaton is defined on the square grid in the following way: each square (“cell”) of the grid can be in one of two states, white or black, and the ant is represented by a short arrow that stands on one cell and points to the north...

Generalized Langton's Ant: Dynamical Behavior and Complexity

Langton’s ant is a simple discrete dynamical system, with a surprisingly complex behavior. We study its extension to general planar graphs. First we give some relations between characteristics of finite graphs and the dynamics of the ant on them. Then we consider the infinite bi-regular graphs of degrees 3 and 4, where we prove the universality of the system, and in the particular cases of the ...

Ethnocultural versus Basic Empathy: Same or Different?

Asymptotic behavior of solutions of general three term recurrence relations

We consider the solutions of general three term recurrence relations whose coefficients are analytic functions in a prescribed region. We study the ratio asymptotic of such solutions under the assumption that the coefficients are asymptotically periodic and their strong asymptotic under more restrictive conditions.