Bernat Espigule

collaborators

4 papers

math.DS2026

Explicit interpolations among the SierpiÅski, Rauzy, and Apollonian gaskets

Bernat Espigule

We study two explicit one-parameter families organized around the affine SierpiÅski gasket. The first is an affine-projective interpolation from the SierpiÅski gasket to the Rauz…

math.DS2026

Infinitely many holes in connectedness loci for collinear affine iterated function systems

Bernat Espigule

We investigate the topology of connectedness loci, denoted as $M_{n}$ , for a one-parameter family of collinear affine iterated function systems featuring equally spaced translations.…

math.DS2026

Finite capture and the closure of roots of restricted polynomials

Bernat Espigule, David Juher

We study how a countable algebraic root set passes to a fractal connectedness locus. Let $D_{n} = {- n + 1, - n + 2, \dots, n - 1}$ , and let $R_{n}$ be the set of roots of monic polynomials whos…

math.DS2024

Collinear Fractals and Bandt's Conjecture

Bernat Espigule, David Juher, Joan SaldaÃ±a

For a complex parameter $c$ outside the unit disk and an integer $n \geq 2$ , we examine the $n$ -ary collinear fractal $E (c, n)$ , defined as the attractor of the iterated function syste…

Explicit interpolations among the SierpiÅski, Rauzy, and Apollonian gaskets

Infinitely many holes in connectedness loci for collinear affine iterated function systems

Finite capture and the closure of roots of restricted polynomials

Collinear Fractals and Bandt's Conjecture

Explicit interpolations among the SierpiÅski, Rauzy, and Apollonian gaskets