Fractals everywhere
Approximations of fractal sets
Journal of Computational and Applied Mathematics
Towards free-form fractal modelling
Proceedings of the international conference on Mathematical methods for curves and surfaces II Lillehammer, 1997
Bounding Recursive Procedural Models Using Convex Optimization
PG '03 Proceedings of the 11th Pacific Conference on Computer Graphics and Applications
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Fractal sets manipulation and modeling is a difficult task due to their complexity and unpredictability. One of the basic problems is to determine bounds of a fractal set given by some recursive definitions, for example by an Iterated Function System (IFS). Here we propose a method of bounding an IFS-generated fractal set by a minimal simplex that is affinely identical to the standard simplex. First, it will be proved that for a given IFS attractor, such simplex exists and it is unique. Such simplex is then used for definition of an Affine invariant Iterated Function System (AIFS) that then can be used for affine transformation of a given fractal set and for its modeling.