# A simple method for estimating the fractal dimension from digital images: The compression dimension

arXiv: https://arxiv.org/abs/1602.02139 · HTML: https://mlsanity.com/paper/1602.02139/

## Key facts

- Cited by 2 papers in the map (data through 14 Oct 2026).
- First posted on arXiv 3 Feb 2016.

## Built on by (most cited first, 2 of 2)

- [Compression ensembles quantify aesthetic complexity and the evolution of visual art](https://mlsanity.com/paper/2205.10271/) (2022)
- [Expertise elevates AI usage: experimental evidence comparing laypeople and professional artists](https://mlsanity.com/paper/2501.12374/) (2025)

## Abstract (arXiv)

The fractal structure of real world objects is often analyzed using digital images. In this context, the compression fractal dimension is put forward. It provides a simple method for the direct estimation of the dimension of fractals stored as digital image files. The computational scheme can be implemented using readily available free software. Its simplicity also makes it very interesting for introductory elaborations of basic concepts of fractal geometry, complexity, and information theory. A test of the computational scheme using limited-quality images of well-defined fractal sets obtained from the Internet and free software has been performed. Also, a systematic evaluation of the proposed method using computer generated images of the Weierstrass cosine function shows an accuracy comparable to those of the methods most commonly used to estimate the dimension of fractal data sequences applied to the same test problem.