<p>Extensions of the classical Hutchinson-Barnsley theory of contractive Iterated Function Systems (IFSs) to more general settings remain a topic of continuous interest at the intersection of IFS theory and fixed point theory. However, most generalizations focus primarily on establishing the existence of a fractal set corresponding to the given IFS, often leaving its computational aspects, fractal measure, and their connections with ergodicity underexplored. This work addresses these gaps by developing a comprehensive framework for IFSs involving <i>F</i>-contractions. We provide a detailed analysis of the associated coding map and invariant measure, completing the Hutchinson-Barnsley theory in this setting. A key contribution is the investigation of the ergodicity of the invariant measure for an IFS with probabilities defined by <i>F</i>-contractions. Additionally, we explore the convergence of forward orbits and other structural properties, offering new insights into the dynamics of such systems. These results deepen the understanding of fractals generated by a certain class of IFS with non-standard contractive maps and contribute to the broader theory of generalized IFS.</p>