The geometry of continued fractions has been studied by numerous mathematicians, in particular through the Farey triangulation and the Ford circles. Recently in 2020, a deformation of continued fractions has been proposed by Morier-Genoud and Ovsienko in algebraic terms. In this talk, I shall present the geometry behind these deformations: the deformed Farey triangulation and a 1-dimensional circle fractal representing rational numbers. An extension to complex numbers leads to partial circle packings in 2d. Joint with Perrine Jouteur and Olga Paris-Romaskevich.