Title: Generalized Moran sets Generated by Step-wise Adjustable Iterated Function Systems,
Abstract: In this article we provide a systematic way of creating generalized Moran
sets using an analogous iterated function system (IFS) procedure. We use a
step-wise adjustable IFS to introduce some variance (such as
non-self-similarity) in the fractal limit sets. The process retains the
computational simplicity of a standard IFS procedure. In our construction of
the generalized Moran sets, we also weaken the fourth Moran Structure Condition
that requires the same pattern of diameter ratios be used across a generation.
Moreover, we provide upper and lower bounds for the Hausdorff dimension of the
fractals created from this generalized process. Specific examples (Cantor-like
sets, Sierpinski-like Triangles, etc) with the calculations of their
corresponding dimensions are studied.