---
type: Fractal Concept
title: Koch Curve
description: Continuous, nowhere-differentiable fractal curve built by recursively replacing each line segment with a four-segment 'bump'.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/classics/koch-curve/
tags:
- classics
- ifs
aliases:
- koch snowflake
- koch
hausdorff_dim_range:
- 1.2619
- 1.2619
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

Continuous, nowhere-differentiable fractal curve built by recursively replacing each line segment with a four-segment 'bump'.

# Aliases

`koch snowflake`, `koch`

# Hausdorff dimension

Approximately **1.2619**.

# Related concepts

* [Fractal](../geometry/fractal.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`