Tight bounding ball for affine IFS attractor

Abstract In this paper we present a new method to compute a ball enclosing an affine IFS attractor in ( R n ,||.||) , where the norm ||.|| is chosen arbitrarily and determines geometry of a ball. The algorithm takes advantage of the first moments of an IFS invariant measure to determine the center of the bounding ball as the attractor's centroid. Then it approximates, at arbitrarily small error, the minimal radius of the ball that is centered at the centroid and encloses the attractor. To obtain a center resulting in a ball that can be referred to as a good approximation of the minimal one, we introduce an iterative method of balancing the attractor. The outcomes supplied by our approach are of the best quality that has been reached so far. Moreover, the algorithm is efficient, easy to implement and not restricted by the dimension of the space occupied by an attractor.

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