---
type: Fractal Concept
title: Box-Counting Dimension
description: Estimated fractal dimension obtained by covering a set with boxes of edge epsilon and measuring how the count N(epsilon) scales as epsilon → 0.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/dimension-theory/box-counting-dimension/
tags:
- dimension-theory
- methods
aliases:
- box counting
- minkowski dimension
- box-counting
sources:
- id: glossary
  resource: https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/
  title: Fractal Notebooks glossary (Chapter 4)
- id: seed
  resource: https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml
  title: fractal_rag concept seed (seed.yaml)
generated:
  by: process:fractal-rag-okf-export
  at: "2026-10-24T00:00:00Z"
status: stable
---

# Definition

Estimated fractal dimension obtained by covering a set with boxes of edge epsilon and measuring how the count N(epsilon) scales as epsilon -> 0.

# Aliases

`box counting`, `minkowski dimension`, `box-counting`

# Related concepts

* [Fractal](../geometry/fractal.md)
* [Fractal Dimension](fractal-dimension.md)

# Citations

[1] [Fractal Notebooks glossary (Chapter 4)](https://tyson-swetnam.github.io/fractal-notebooks/foundations/glossary/) — `docs/foundations/glossary.md`

[2] [fractal_rag concept seed (seed.yaml)](https://github.com/tyson-swetnam/fractal-notebooks/blob/main/fractal_rag/src/fractal_rag/concepts/seed.yaml) — `fractal_rag/src/fractal_rag/concepts/seed.yaml`