Sequences of complex numbers resembling the Fibonacci series

Each term of the classical Fibonacci sequence of numbers is the sum of the two previous terms of the sequence. If instead of the sum the third term is an addition or a subtraction of the two previous terms, one of them multiplied by a constant, new and rich sequences are obtained. Some of the properties of these sequences are herein studied by means of numerical procedures, incorporating the condition that each term, including the constant, are complex number

Self-avoiding random walkers with steps along eight possible directions (octopus walkers)

Diferent types of random walkers are studied by assuming that they have eight diferent possibilities to make steps in pre-determined directions. The walkers are not allowed to step on already visited places in the plane (self-avoiding walkers). The main variables chosen to depict their behavior are the number of steps and the distance they reach before they are trapped. A measure of how the walkers are difused, an index of how the paths of the walkers are folded and the efect of restricting the region where the walkers may walk are also studied.