Contrasts in the basins of attraction of structurally identical iterative root finding methods

A numerical comparison is performed between three methods of third order with the same structure, namely BSC, Halley’s and Euler–Chebyshev’s methods. As the behavior of an iterative method applied to a nonlinear equation can be highly sensitive to the starting points, the numerical comparison is carried out, allowing for complex starting points and for complex roots, on the basins of attraction in the complex plane. Several examples of algebraic and transcendental equations are presented.

A Representação de Personagens Virtuais: Como a Tecnologia Obriga à Criação de Estilos e Estéticas Interdisciplinares na Animação Contemporânea

The evolution of computer animation represents one of the most relevant andrevolutionary aspects in the rise of contemporary digital visual culture (Darlew,2000), in particular, phenomena such as cinema “spectacular “ (Ibidem) and videogames. This article analyzes the characteristics of this “culture of simulation” (Turkle, 1995:20) relating the multidisciplinary and spectrum of technical and stylistic choices to the dimension of virtual characters acting. The result of these hybrid mixtures and computerized human motion capture techniques - called virtual cinema, universal capture, motion capture, etc. - cosists mainly on the sophistication of “rotoscoping”, as a new interpretation and appropriation of the captured image. This human motion capture technology, used largely by cinema and digital games, is one of the reasons why the authenticity of the animation is sometimes questioned. It is in the fi eld of 3D computer animation visual that this change is more signifi cant, appearing regularly innovative techniques of image manipulation and “hyper-cinema” (Lamarre, 2006: 31) character’s control with deeper sense of emotions. This shift in the culture that Manovich (2006: 27) calls “photo-GRAPHICS” - and Mulvey (2007) argue that creates a new form of possessive relationship with the viewer, in that it can analyze in detail the image, it can acquire it and modify it - is one of the most important aspects in the rise of Cubbit’s (2007) “cinema of attraction”. This article delves intrinsically into the analyze of virtual character animation — particularly in the fi eld of 3D computer animation and human digital acting.