CRITICISM INSTRUMENTS

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CONTEMP ART ‘12

CRITICISM INSTRUMENTS ANTÓNIO PEDRO A. N. L. LIMA F.C.T. - Fundação para a Ciência e a Tecnologia C.I.A.U.D. - Centro de Investigação em Arquitectura, Urbanismo e Design Universidade Técnica de Lisboa - Faculdade de Arquitectura António Pedro A. N. L. Lima, Ph.D. E-mail: arq.lima@gmail.com Summary Examples of objects with scale properties and non integre dimension have long been known to mathematicians but it was Benoit Mandelbrot [1] who, introducing the term fractal, first classified such kind of objects, providing a scientific basis for the study of irregular sets. One of the characteristics of these objects is their fractal dimension and one of the methods to determine this dimension is the “box-counting dimension” technique that, for real objects, provides a very good approximation to the determination of this non-topological dimension. This technique is applied covering any two-dimensional representation with a squared mesh and counting the number of boxes containing lines from it knowing that, the tighter the grid, the greater the number of boxes containing lines from the given representation. Being A a one-dimensional object, covered by a squared mesh size є, N(є) represents the number of boxes that contain lines belonging to A. Thus, if D = lim log N (ε ) exists, then D is the box-counting dimension of A, fig. 1. ε→0 log(1/ε) Introduction

Figure 1: First four stages of the box-countig dimension calculation on a von Koch curve. 41


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