# Crocheting the Lorenz Manifold

@article{Osinga2004CrochetingTL, title={Crocheting the Lorenz Manifold}, author={Hinke M. Osinga and Bernd Krauskopf}, journal={The Mathematical Intelligencer}, year={2004}, volume={26}, pages={25-37} }

You have probably seen a picture of the famous butterfly-shaped Lorenz attractor — on a book cover, a conference poster, a coffee mug or a friend’s T-shirt. The Lorenz attractor is the best known image of a chaotic or strange attractor. We are concerned here with its close cousin, the two-dimensional stable manifold of the origin of the Lorenz system, which we call the Lorenz manifold for short. This surface organizes the dynamics in the three-dimensional phase space of the Lorenz system. It is…

## 32 Citations

Visualizing curvature on the Lorenz manifold

- Physics
- 2007

The Lorenz manifold is an intriguing two-dimensional surface that illustrates chaotic dynamics in the well-known Lorenz system. While it is not possible to find an explicit analytic expression for…

Global bifurcations of the Lorenz manifold

- Mathematics
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In this paper we consider the interaction of the Lorenz manifold—the two-dimensional stable manifold of the origin of the Lorenz equations—with the two-dimensional unstable manifolds of the secondary…

How to Crochet a Space-Filling Pancake: the Math, the Art and What Next

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The chaotic behavior of the famous Lorenz system is organized by an amazing surface: the Lorenz manifold. Initial conditions on different sides of this surface will behave differently after some…

The Lorenz manifold: Crochet and curvature

- Physics
- 2006

We present a crocheted model of an intriguing two-dimensional surface — known as the Lorenz manifold — which illustrates chaotic dynamics in the well-known Lorenz system. The crochet instructions are…

Visualizing the transition to chaos in the Lorenz system

- Physics
- 2006

The Lorenz system still fascinates many people because of the simplicity of the equations that generate such complicated dynamics on the famous butterfly attractor. This paper addresses the role of…

Visualizing global manifolds during the transition to chaos in the Lorenz system

- MathematicsTopology-Based Methods in Visualization II
- 2009

This work discusses an algorithm for computing global manifolds of vector fields that is decidedly geometric in nature, and allows to visualize the resulting surface by making use of the geodesic parametrization.

The Sculpture Manifold: A Band from a Surface, a Surface from a Band

- Art
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The steel sculpture Manifold consists of an 8 cm wide closed band of stainless steel that winds around in an intricate way, curving and coming very close to itself. It is based on a complicated…

Investigating the consequences of global bifurcations for two-dimensional invariant manifolds of vector fields

- Mathematics
- 2010

We consider a homoclinic bifurcation of a vector field in $\R^3$,
where a one-dimensional unstable manifold of an equilibrium is
contained in the two-dimensional stable manifold of this same …

Computation and visualization of invariant manifolds

- Computer Science
- 2009

This thesis starts with the basic concepts of dynamical systems, then introduces the general types of problems that the well-known software package AUTO solves, and discusses the basic bifurcation and stability analysis of general ODE systems.

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