Volume 65, pp. 1-25, 2026.

Fractal approximations on the real projective plane

Alamgir Hossain, Md. Nasim Akhtar, and M. A. Navascués

Abstract

The study of the fractal theory in Euclidean spaces has recently emerged as an intriguing research area. The concept of fractal interpolation yields a method to approximate functions that are both self-affine or non-self-affine and consequently allows substantial flexibility and diversity of the fractal modeling problem. In this article, we introduce non-affine fractal functions on the non-Euclidean real projective plane. To do so, a real projective plane with a linear structure is considered. Then we study some classical approximation results for it. After considering a suitable iterated functions system (IFS) on the real projective plane, we construct non-affine fractal functions on it. Some fractal versions of classical approximation results are proved for the projective plane. Moreover, we prove that the attractor of an IFS on the dual space of the real projective plane is also the graph of a fractal function.

Full Text (PDF) [527 KB], BibTeX , DOI: 10.1553/etna_vol65s1

Key words

real projective iterated function system, fractal interpolation, $\alpha$-fractal functions, approximations, dual fractal functions

AMS subject classifications

28A80, 41A05

Links to the cited ETNA articles

[16]	Vol. 20 (2005), pp. 64-74 M. A. Navascues: Fractal trigonometric approximation
[24]	Vol. 41 (2014), pp. 420-442 Puthan Veedu Viswanathan and Arya Kumar Bedabrata Chand: $\alpha$-fractal rational splines for constrained interpolation
[25]	Vol. 44 (2015), pp. 639-659 Puthan Veedu Viswanathan and Arya Kumar Bedabrata Chand: Monotone-Comonotone approximation by fractal cubic splines and polynomials