---
type: Fractal Concept
title: Mandelbrot Set
description: Set of complex numbers c for which the orbit of 0 under z → z^2 + c remains bounded.
resource: https://tyson-swetnam.github.io/fractal-notebooks/okf/concepts/complex-dynamics/mandelbrot-set/
tags:
- complex-dynamics
- classics
aliases:
- mandelbrot
hausdorff_dim_range:
- 2.0
- 2.0
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

Set of complex numbers c for which the orbit of 0 under z -> z^2 + c remains bounded. Its boundary is a quintessential 2D fractal.

# Aliases

`mandelbrot`

# Hausdorff dimension

Approximately **2.0**.

# 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`