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- Philip Glass' Façades: a case study on the complexity of music scoresPublication . Pestana, Pedro Duarte; Pestana, DinisRepetitive structures in the soprano saxophones, violas/synthesizer and violoncelli in the full score of Philip Glass' Fa cades [4] are investigated assimilating similar music bars with the axial-diagonal self-a ne cartoons as de ned by Mandelbrot [7], [8] to construct very general multi-fractals. Transition matrices of order 1 Markov chains are used to simulate surrogates of phrases of the same piece, to investigate whether in this minimalist setting we obtain (i) an exact reproduction of the original, or (ii) something that though di erent sounds a pleasant variation.
- Sir Pinski rides againPublication . Gomes, Maria Ivette; Pestana, Dinis; Pestana, PedroThe iterative procedure of removing “almost everything” from a triangle ultimately leading to the Sierpinski's gasket S is well-known. But what is in fact left when almost everything has been taken out? Using the Sir Pinski's game described by Schroeder [4], we identify two dual sets of invariant points in this exquisite game, and from these we identify points left over in Sierpinski gasket. Our discussion also shows that the chaos game does not generate the Sierpinski gasket. It generates an approximation or, at most, a subset of S.
- Sir Pinski Rides AgainPublication . Gomes, Maria Ivette; Pestana, Dinis; Pestana, Pedro DuarteThe iterative procedure of removing “almost everything” from a triangle ultimately leading to the Sierpinski's gasket S is well-known. But what is in fact left when almost everything has been taken out? Using the Sir Pinski's game described by Schroeder [4], we identify two dual sets of invariant points in this exquisite game, and from these we identify points left over in Sierpinski gasket. Our discussion also shows that the chaos game does not generate the Sierpinski gasket. It generates an approximation or, at most, a subset of S.