THE IMPRESSIVE COMPLEXITY IN THENAUTILUS POMPILIUSSHELL

Abstract

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.

The Fractal Dimension of an Oil Spray

“…We have used the well-know box-counting method to calculate the fractal dimension of the spray contour: a grid of size ε is superimposed on the black and white images and then, the boxes of this grid that intersect any part of the image are counted to provide the number N ; the process is repeated reducing the size of the grid and thus, the discrete function N (ε) is generated. The initial size is usually a one pixel grid [7,8,9] and the number of pixels of size 1/ε is increased until the grid size reaches a certain previously determined value (this value is usually given by the smallest possible pixel size). Finally, one is interested in the limit…”