# Abstract Fractals

## TL;DR

This paper introduces a novel, more general definition of fractals based on conditions governing subsets of metric spaces, expanding the scope of fractal and chaos theory research.

## Contribution

It proposes a new, more inclusive definition of fractals that encompasses a broad class of self-similar structures, advancing theoretical understanding.

## Key findings

- The new definition captures a large class of self-similar fractals.
- Examples confirm the applicability of the definition.
- Creates new avenues for fractal and chaos research.

## Abstract

We develop a new definition of fractals which can be considered as an abstraction of the fractals determined through self-similarity. The definition is formulated through imposing conditions which are governed the relation between the subsets of a metric space to build a porous self-similar structure. Examples are provided to confirm that the definition is satisfied by large class of self-similar fractals. The new concepts create new frontiers for fractals and chaos investigations.