The present work is splitted into two parts. In the first one we present the generalized logarithm and exponential functions. From them, a wide variety of other generalized functions can be obtained, that allow a unique formulation of oscillatory, exponential an power-law behaviors, that characterize physical phenomena. We also show that it is possible to generalize the stretched exponential probability density function (pdf) and, from there, a wide range of other pdf's that characterize complex systems in Physics. The generalized logarithm and exponential functions are also useful to generalize several continuous growth models into a single formulation: the generalized Tsoullaris and Wallace growth model. The same can be done for discrete growth models, getting, as more general model, the generalized θ-Ricker growth model. Concluding the first part, we show that the generalized Gaussian pdf (a special case of the generalized stretched exponential) is a solution of the nonlinear diffusion equation, which is a characteristic of deterministic tourist walk. In the second part we present the tourist walk and its two original versions: the deterministic one (DTW) and stochastic one (STW). The first one is a partially self-avoiding walk over a disordered multidimensional medium formed by N points and characterized by a memory µ. In a one-dimensional environment, it presents a transition from a local exploration to a global one at a well-defined memory value µ 1 = log 2 N. In its stochastic version (from which DTW is a particular case), the movement dynamics is ruled by the memory µ and a temperature T which is responsible by the displacement probabilities. Similar to DTW, STW also has a transition between exploration schemes, characterized by a critical memory and temperature and the walking age (N p) (aging effect). Due the difficulty on analytical treatment of the CET, we introduced the modified stochastic tourist walk (MSTW). In this version, the parameter T plays the role of a maximum distance of one walking step. This modification allowed us to treat analytically the walk, being possible to obtain a general analytical expression for the transition, as function to the parameters µ, T and N p. These results were validated by numerical experiments.