The complexity of the Nautilus pompilius shell is analyzed in terms of its fractal dimension and its equiangular spiral form. Our findings assert that the shell is fractal from its birth and that its growth is dictated by a self-similar criterion (we obtain the fractal dimension of the shell as a function of time). The variables that have been used for the analysis show an exponential dependence on the number of chambers/age of the cephalopod, a property inherited from its form.

A method for interpreting elastic-lidar return signals in heavily-polluted atmospheres is presented. It is based on an equation derived directly from the classic lidar equation, which highlights gradients of the atmospheric backscattering properties along the laser optical path. The method is evaluated by comparing its results with those obtained with the differential absorption technique. The results were obtained from locating and ranging measurements in pollutant plumes and contaminated environments around central México.

While conducting a study with air in a simple closed rectangular cavity, we have discovered the formation of highly impressive, complex-structured, and symmetrical smoke density patterns. Using the box counting method the fractal characteristic of the patterns is demonstrated.

Breather stability and longevity in thermally relaxing nonlinear arrays is investigated under the scrutiny of the analysis and tools employed for time series and state reconstruction of a dynamical system. We briefly review the methods used in the analysis and characterize a breather in terms of the results obtained with such methods. Our present work focuses on spontaneously appearing breathers in thermal Fermi-Pasta-Ulam arrays but we believe that the conclusions are general enough to describe many other related situations; the particular case described in detail is presented as another example of systems where three incommensurable frequencies dominate their chaotic dynamics (reminiscent of the Ruelle-Takens scenario for the appearance of chaotic behavior in nonlinear systems). This characterization may also be of great help for the discovery of breathers in experimental situations where the temporal evolution of a local variable (like the site energy) is the only available/measured data.