On Intersecting IFS Fractals with Lines

IFS Fractals the attractors of Iterated Function Systems in Euclidean space have motivated plenty of investigation to date, due to their simplicity and applicability in various fields, such as the modeling of plants in computer graphics, and the design of fractal antennas. The statement and resolution of the Fractal-Line Intersection Problem is imperative for a more efficient treatment of applications. This paper intends to take further steps towards this resolution, building on the literature. We provide a verifiable condition guaranteeing intersection with any line passing through the convex hull of an IFS fractal, shown in Rd for hyperplanes. The condition also implies a constructive algorithm for finding the points of intersection. We give several numerical conditions that guarantee an infinite number of approximate intersections if there is at least one. In our effort to quantify the intersection, we provide an explicit formula for the well-known invariant measure of IFS.∗ MSC class: 28A80 (primary); 37F99, 52A35 (secondary)