ON ATTRACTORS OF TYPE 1 ITERATED FUNCTION SYSTEMS †

. This paper discusses the properties of attractors of Type 1 IFS which construct self similar fractals on product spaces. General results like continuity theorem and Collage theorem for Type 1 IFS are established. An algebraic equivalent condition for the open set condition is studied to characterize the points outside a feasible open set. Connectedness properties of Type 1 IFS are mainly discussed. Equivalence condition for connectedness, arc wise connectedness and locally connectedness of a Type 1 IFS is established. A relation connecting separation properties and topological properties of Type 1 IFS attractors is studied using a generalized address system in product spaces. A construction of 3D fractal images is proposed as an application of the Type 1 IFS theory.