2 citations · 4 across the 6 of their papers we have counts for
6 papers
Explicit interpolations among the Sierpiński, Rauzy, and Apollonian gaskets
Bernat Espigule
We study two explicit one-parameter families organized around the affine Sierpiński gasket. The first is an affine-projective interpolation from the Sierpiński gasket to the Rauzy…
Infinitely many holes in connectedness loci for collinear affine iterated function systems
Bernat Espigule
We investigate the topology of connectedness loci, denoted as , for a one-parameter family of collinear affine iterated function systems featuring equally spaced translations.…
Semialgebraic interior layers in root closures of bounded-height integer polynomials
Bernat Espigule, David Juher
Finite-degree root plots of bounded-height monic integer polynomials can exhibit gaps around interior points of their root closures. Outside the closed unit disk, these closures co…
Collinear Fractals and Bandt's Conjecture
Bernat Espigule, David Juher, Joan Saldaña
For a complex parameter outside the unit disk and an integer , we examine the -ary collinear fractal , defined as the attractor of the iterated function syste…
A family of fern-like ternary complex trees
Bernat Espigule
A ternary complex tree related to the golden ratio is used to show how the theory of complex trees works. We use the topological set of this tree to obtain a parametric family of t…
Families of connected self-similar sets generated by complex trees
Bernat Espigule
The theory of complex trees is introduced as a new approach to study a broad class of self-similar sets. Systems of equations encoded by complex trees tip-to-tip equivalence relati…