Fractal Stochastic Processes on Thin Cantor-Like Sets

Classifying Cantor Sets by Their Fractal Dimensions

In this article we study Cantor sets defined by monotone sequences, in the sense of Besicovich and Taylor. We classify these Cantor sets in terms of their h-Hausdorff and h-packing measures, for the family of dimension functions h, and characterize this classification in terms of the underlying sequences.

Thin Sets with Fat Shadows: Projections of Cantor Sets

A Cantor set is a nonempty, compact, totally disconnected, perfect subset of IR. Now, the set being totally disconnected means that it is scattered about like a “dust”. If you shine light on a clump of dust floating in the air, the shadow of this dust will look like a bunch of spots on the wall. You would be very surprised if you saw that the shadow was a filled-in shape (like a rabbit, say!). ...

New 5-adic Cantor sets and fractal string

In the year (1879-1884), George Cantor coined few problems and consequences in the field of set theory. One of them was the Cantor ternary set as a classical example of fractals. In this paper, 5-adic Cantor one-fifth set as an example of fractal string have been introduced. Moreover, the applications of 5-adic Cantor one-fifth set in string theory have also been studied.

Optimal quantization for uniform distributions on Cantor-like sets

In this paper, the problem of optimal quantization is solved for uniform distributions on some higher dimensional, not necessarily self-similar N−adic Cantor-like sets. The optimal codebooks are determined and the optimal quantization error is calculated. The existence of the quantization dimension is characterized and it is shown that the quantization coefficient does not exist. The special ca...

On the Dimension of Deterministic and Random Cantor-like Sets