Showing papers on "Affine involution published in 1990"
27 Aug 1990
TL;DR: It is shown that PAA are capable of generating highly complex images and Barnsley's IFS method to generate fractals is a special case of PAA when the automaton happens to have only a single state.
Abstract: In this paper, we introduce probabilistic affine automata (PAA) which are probabilistic finite generators having transitions labeled with affine transformations. It is shown that PAA are capable of generating highly complex images. Barnsley's IFS method to generate fractals is a special case of PAA when the automaton happens to have only a single state.
15 citations
TL;DR: In this paper, the surface area and volume of a convex compact subset of ℝ d are denoted s ( K ) and v ( K ), respectively, and the support function of the convex body K is denned by h ( K, x ) = max y∈K x t y and the polar dual of K 0 = { x: |x t y|1, y ∈K }.
Abstract: A convex compact subset of ℝ d is called a convex body. The (Euclidean) surface area and volume of a convex body K are denoted s ( K ) and v ( K ) respectively. The support function of a convex body K is denned by h ( K, x ) = max y∈K x t y and the polar dual of K is given by K 0 = { x: |x t y|1, y∈K }. Double vertical bars shall denote the Euclidean length of a vector , and S shall denote the unit sphere (the Euclidean unit ball): S = {x: ║x║≤1}. We use for the mixed volume
6 citations
TL;DR: In this article, it was shown that for affine mappings this dependency can be described by solutions of certain linear equations, which can be expressed as linear equations in terms of linear equations.
Abstract: Suppose the mapping T has more then one fixed point. If the iteration converges, the limit will depend on the choice of the starting point. It is shown that for affine mappings this dependency can be described by solutions of certain linear equations.
1 citations