Redundancy in Cantor Diffractals

Redundancy in Cantor diffractals.

Cantor diffractals are waves that have encountered a Cantor grating. In this paper, we report an important property of Cantor diffractals, namely that of redundancy. We observe that the Fraunhofer diffraction pattern comprises of several bands, each containing complete information about the fractal aperture. This redundancy allows for a faithful reconstruction ...

Robustness of Cantor diffractals.

Diffractals are electromagnetic waves diffracted by a fractal aperture. In an earlier paper, we reported an important property of Cantor diffractals, that of redundancy [R. Verma et. al., Opt. Express 20, 8250 (2012)]. In this paper, we report another important property, that of robustness. The question we address is: How much disorder in the Cantor grating can be accommodated by diffractals to...

Cantor knots

A technique based on Cantor division is used to embellish artistic knotwork designs. Weaving rules are relaxed to allow a mostly alternating weave to be applied to the resulting patterns. The new method is compared to traditional knotwork, and the generation of examples is discussed. r 2005 Elsevier Ltd. All rights reserved.

Cantor sets

This paper deals with questions of how many compact subsets of certain kinds it takes to cover the space ω of irrationals, or certain of its subspaces. In particular, given f ∈ (ω\{0}), we consider compact sets of the form Q i∈ω Bi, where |Bi| = f(i) for all, or for infinitely many, i. We also consider “n-splitting” compact sets, i.e., compact sets K such that for any f ∈ K and i ∈ ω, |{g(i) : ...

Cantor goes