A new algorithm that generates the image of the attractor of a generalized iterated function system

Approximating the Attractor Set of Iterated Function Systems of Order m by $$\alpha $$-Dense Curves

“…The concept of iterated function systems, IFS, to construct fractals was introduced by Hutchinson [12] in the decade 1980-1990, and later popularized by Barnsley [3]. Due to the applications of the fractals in many applied sciences (see, for instance, [7,8,14,29,36] and references therein), the IFS have been widely studied; see [2,6,11,13,15,[17][18][19][20]28,[30][31][32][33][34].…”

“…, A) = A. As in the case of the IFS of order m, for a given CIFS of order m always, there exists an attractor set and it is unique (see, for instance, [19,30]). Next, we have the following result for a CIFS (see, for instance, [32, Theorem 3.9]): Proposition 1.2.…”

Making the computation of approximations of invariant measures and its attractors for IFS and GIFS, through the deterministic algorithm, tractable

“…obtained by the updating rule (7). The first coordinates of D N , given by supp(M N +1 S (µ)) approximate the attractor set A S , and the second coordinates {v 1 , ..., v m }, gives the value at each point of the discrete probability M N S (µ) approximating the invariant idempotent probability µ S .…”

“…As can be seen in [4,5,7] and [6,8] the discrete algorithms exhibit a good performance, but require a lot of technical detail to its implementation. On the other hand deterministic algorithms are easy to describe and implement, in its naive version, but they are impractical computationally.…”

A multiresolution algorithm to generate images of generalized fuzzy fractal attractors

“…Through the years several papers has been published providing algorithms generating attractors for IFS, see [dAICMDCNAS03], [Mic10b], [Elq90], [Yan94] etc, for fuzzy IFS, see [Vrs92], etc, and lately for GIFS see [Str16], [MMU19], etc.…”